Website
Dean
James L. Kays, Ph.D., BG, USA, (Ret.)
Naval Postgraduate School
Code 07, Spanagel Hall, Room 103
833 Dyer Road,
Monterey, CA 93943-5117
(831) 656-7859, DSN 756-7859, FAX (831) 656-7861
Associate Dean
Christopher Adams, CDR, USN
Code 07B, Spanagel Hall, Room 103
(831) 656-2682, DSN 756-2682, FAX (831) 656-7861
The Graduate School of Engineering and Applied Sciences consist of seven Departments, two Committees, and one Academic Group:
Department of Applied Mathematics |
MA |
Department of Electrical and Computer Engineering |
ECE |
Engineering Acoustics Academic Committee |
EAAC |
Department of Mechanical and Astronautical Engineering |
MAE |
Department of Meteorology |
MR |
Department of Oceanography |
OC |
Department of Physics |
PH |
Space Systems Academic Group |
SP |
Department of Systems Engineering |
SE |
Undersea Warfare Academic Committee |
UWAC |
Overview
The Graduate School of Engineering and Applied Sciences (GSEAS) supports the Navy and the Department of Defense by educating future leaders to lead, innovate and manage in a changing, highly technological world, and by conducting research recognized internationally for its relevance to national defense and academic quality. More specifically, GSEAS provides advanced technical and scientific knowledge and understanding so graduates:
GSEAS accomplishes the above by offering high quality, traditional academic degrees that include:
Curricula
Traditional degree granting programs are offered by departments, normally at both the master's and Ph.D. levels. Most of these degree programs are an integral part of one or more unique interdisciplinary curricula designed for relevance to national security needs. Each of these curricula infuses cutting edge knowledge into academic courses taught by a dedicated, world-class faculty:
Applied Mathematics (380)
Combat Systems Sciences and Technology (533)
Electronic Systems Engineering (590)
MAE Reactors/Mechanical Engineering (Distance Learning) (571)
Mechanical & Astronautical Engineering (570)
Meteorology (372)
Meteorology and Oceanography (373)
Oceanography (440)
Operational Oceanography (374)
Space Systems Engineering (591)
Space Systems Operations (366) *
Space Systems Operations (Distance Learning) (316)*
Space Systems Operations (International) (364)
Systems Engineering (580)
Systems Engineering and Analysis (308) *
Systems Engineering Certificate (282)
Systems Engineering (Distance Learning) (311) *
Systems Engineering Management (MSSEM) / Product Development (Distance Learning) (721)
Underwater Acoustics (Distance Learning) (535)
Undersea Warfare (525) *
Undersea Warfare (International) (526) *
*Indicates an interdisciplinary curriculum offered with the Graduate School of Operations and Information Sciences
Degrees
Within each of these curricula, students have the opportunity to earn a high quality academic degree while focusing on an area relevant to national defense and war fighting capabilities. For example, a student enrolled in Space Systems Engineering (Curriculum 591) has an opportunity to study and do research related to space systems while earning an academic degree from either the Department of ECE, PH, MAE, SE or CS (Computer Science). Student research is under the tutelage of faculty with research experience related to national security and is an integral part of the educational experience of each student.
GSEAS offers the following degree programs, each designed and evolved to meet the changing needs of the Navy and defense communities while maintaining high academic standards:
Master of Science in Applied Mathematics, Ph.D. in Applied Mathematics
Master of Science in Applied Physics, Ph.D. in Applied Physics
Master of Science in Applied Science
Master of Science in Astronautical Engineering, Astronautical Engineer, Ph.D. in Astronautical Engineering
Master of Science in Combat Systems Technology
Master of Science in Electrical Engineering, Electrical Engineer, Ph.D. in Electrical & Computer Engineering
Master of Science in Engineering Acoustics, Ph.D. in Engineering Acoustics
Master of Science in Engineering Science
Master of Science in Mechanical Engineering, Mechanical Engineer, Ph.D. in Mechanical Engineering
Master of Science in Meteorology, Ph.D. in Meteorology
Master of Science in Meteorology and Physical Oceanography
Master of Science in Physical Oceanography, Ph.D. in Physical Oceanography
Master of Science in Physics, Ph.D. in Physics
Master of Science in Systems Engineering
Master of Science in Systems Engineering and Analysis
Chairman
Clyde Scandrett, Ph.D.
Code MA, Spanagel Hall, Room 254
(831) 656-3973, DSN 756-3973, FAX (831) 656-2355
Associate Chairman, Labs and Computing
David R. Canright, Ph.D.
Code MA/Ca, Spanagel Room 246
(831) 656-2782, DSN 756-2782
Associate Chairman, Research
Carlos F. Borges, Ph.D.
Code MA/Bc, Spanagel Room 242B
(831) 656-2124, DSN 756-2124
Associate Chairman, Instruction
Bard Mansager, M.A.
Code MA/Ma, Spanagel Room 248B
(831) 656-2695, DSN 756-2695
Carlos Borges, Professor and Associate Chair for Research (1991)*; Ph.D., University of California, Davis, 1990.
David Canright, Associate Professor and Associate Chair for Labs and Computing (1988); Ph.D., University of California at Berkeley, 1987.
Lester E. Carr, III, Lecturer (2005); Ph.D., Naval Postgraduate School, 1989.
Donald Alfred Danielson, Professor (1985); Ph.D., Harvard University, 1968.
Doyle Daughtry, Lecturer (2004); MA, East Carolina University, 1973.
Fariba Fahroo, Professor (1992); Ph.D., Brown University, 1991.
Harold M. Fredricksen, Professor (1980); Ph.D., University of Southern California, 1968.
Christopher Frenzen, Associate Professor (1989); Ph.D., University of Washington, 1982.
Ralucca Gera, Assistant Professor (2005); Ph.D., Western Michigan University, 2005.
Frank Giraldo, Associate Professor (2006); Ph.D., University of Virginia, 1995.
William Gragg, Professor (1987); Ph.D., University of California at Los Angeles, 1964.
Wei Kang, Professor (1994); Ph.D., University of California at Davis, 1991.
Arthur Krener, Distinguished Visiting Professor (2006); Ph.D., University of California at Berkeley, 1971
Bard Mansager, Senior Lecturer and Associate Chair for Instruction and Academic Associate(1991); M.A., University of California, San Diego, 1979.
Beny Neta, Professor, (1985); Ph.D., Carnegie-Mellon University, 1977.
Guillermo Owen, Distinguished Professor (1983); Ph.D., Princeton University, 1962.
Craig Rasmussen, Associate Professor (1991); Ph.D., University of Colorado at Denver, 1990.
Clyde Scandrett, Professor (1987); Ph.D., Northwestern University, 1985.
Pantelimon Stanica, Associate Professor (2006); Ph.D., State University of New York at Buffalo, 1998.
Hong Zhou, Associate Professor (2004); Ph.D., University of California at Berkeley, 1996.
Professors Emeriti:
Richard Franke, Professor Emeritus (1970); Ph.D., University of Utah, 1970.
Toke Jayachandran, Professor Emeritus (1967); Ph.D., Case Institute of Technology, 1967.
Gordon E. Latta, Professor Emeritus (1979); Ph.D., California Tech, 1951.
Arthur L. Schoenstadt, Professor Emeritus (1970); Ph.D., Rensselaer Polytechnic Institute, 1968.
Maurice Dean Weir, Professor Emeritus (1969); D.A., Carnegie-Mellon University, 1970.
* The year of joining the Naval Postgraduate School faculty is indicated in parentheses.
Brief Overview
As well as the Master of Science and Ph.D. programs in Applied Mathematics, the Applied Mathematics Department offers individually tailored minor programs for many of the school's doctoral students. The majority of the department instructional—effort is devoted to the service courses offered.
Degrees
Master of Science in Applied Mathematics
In order to enter a program leading to the degree Master of Science in Applied Mathematics, the prospective student is strongly advised to posses either a Bachelor degree with a major in mathematics or a strong mathematical orientation in a Bachelor degree in another discipline.
Any program that leads to the degree Master of Science in Applied Mathematics for a student who has met the entrance criteria must contain a minimum of 32 quarter-hours of graduate-level (3000-4000 numbered) courses with a minimum QPR of 3.0. The program specifications must be approved by the Chairman of the Department of Applied Mathematics and the Academic Associate. The program is subject to the general conditions specified in the Academic Council Policy Manual as well as the following:
In addition to the core courses required in item (3), the program allows the student to select an applied subspecialty option from the following list: applied mathematics, numerical analysis and computation, discrete mathematics, operations research, theoretical mathematics, and intelligence.
Doctor of Philosophy
The Department of Applied Mathematics offers the Doctor of Philosophy in Applied Mathematics degree. Areas of specialization will be determined by the department on a case by case basis. Requirements for the degree include course work followed by an examination in both major and minor fields of study, and research culminating in an approved dissertation. It may be possible for the dissertation research to be conducted off-campus in the candidate's sponsoring organization.
Entrance into the program will ordinarily require a master's degree, although exceptionally well-prepared students with a bachelor's degree in mathematics may be admitted. A preliminary examination may be required to show evidence of acceptability as a doctoral student. Prospective students should contact the Chairman of the Applied Mathematics Department or the Academic Associate for further guidance.
NPS Academic Certificate Program (Mathematics of Secure Communication - Curriculum 280)
The Mathematics of Secure Communication certificate program comprises four courses (MA3025, MA3560, MA4560, and MA4570), designated below by an asterisk. Upon successful completion of the coursework, students will be awarded a certificate of accomplishment, in keeping with standard practices of the Naval Postgraduate School. The purpose of this program is to provide mathematics education to naval officers and DoD civilians in the broad area of Cryptography and Secure Communications.
Prerequisites
Prerequisites are as described in the course descriptions. If a student has not taken the prescribed prerequisites at NPS, then a validation examination by the Applied Mathematics Department may be substituted.
Place-holder. Do not remove.
MA0134 Problem Solving Session for MA1113/4 (No Credit) (0-3) Spring/Summer/Fall/Winter
Offered for no credit, pass/fail. Students must be concurrently enrolled in either MA1113 or MA1114, but the course is not mandatory for either course. Prerequisites: None.
MA0156 Problem Solving Session for MA1115/6 (No Credit) (0-3) Spring/Summer/Fall/Winter
Offered for no credit, pass/fail. Students must be concurrently enrolled in either MA1115 or MA1116, but the course is not mandatory for either course. Prerequisites: None.
MA0810 Thesis Research (0-8) As Required
Every student conducting thesis research will enroll in this course. Prerequisites: None.
MA1010 Algebra and Trigonometry (4-0) As Required
Real number system, complex numbers, exponents and radicals, algebraic expressions and operations, linear and quadratic equations, inequalities, functions and graphs, polynomials and their zeros, rational functions, exponential and logarithmic functions, systems of equations, matrices, trigonometry and unit circles, trigonometric identities and functions. Prerequisites: None.
MA1025 Introduction to Mathematical Reasoning (4-0) As Required
An introductory course in logic and elementary discrete mathematics to be taken by students in the Operations Research curriculum. Considerable emphasis is placed on propositional and predicate logic, and on techniques of proof in mathematics. Mathematical topics include sets, functions, and relations. Coverage of combinatorics includes an introduction to permutations, combinations, the pigeon-hole principle, and the principle of inclusion/exclusion. No previous experience with this material is assumed. Prerequisites: None.
MA1113 Single Variable Calculus (4-0) Spring/Summer/Fall/Winter
Review of analytic geometry and trigonometry, functions of one variable, limits, derivatives, continuity and differentiability; differentiation of algebraic, trigonometric, logarithmic and exponential functions with applications to maxima and minima, rates, differentials; product rule, quotient rule, chain rule; antiderivatives, integrals and the fundamental theorem of calculus; definite integrals, areas. Taught at the rate of nine hours per week for five weeks. Prerequisites: Pre-Calculus mathematics.
MA1114 Single Variable Calculus II with Matrix Algebra (4-0) Spring/Summer/Fall/Winter
Topics in calculus include applications of integration, special techniques of integration, infinite series, convergence tests, and Taylor series. Matrix algebra topics covered are: the fundamental algebra of matrices including addition, multiplication of matrices, multiplication of a matrix by a constant and a column (vector) by a matrix; elementary matrices and inverses, together with the properties of these operations; solutions to mxn systems of linear algebraic equations using Gaussian elimination and the LU decomposition (without pivoting); determinants, properties of determinants; and a brief introduction to the arithmetic of complex numbers and DeMoivre's theorem. Taught at the rate of nine hours per week for five weeks. Prerequisites: MA1113.
MA1115 Multi Variable Calculus (4-0) Spring/Summer/Fall/Winter
Vector algebra and calculus, directional derivative, gradient, polar coordinates and parametric equations, functions of several independent variables, limits, continuity, partial derivatives, chain rule, maxima and minima, double and triple integrals, cylindrical and spherical coordinate systems. Taught at the rate of nine hours per week for five weeks. Prerequisites: MA1114.
MA1116 Vector Calculus (3-0) Spring/Summer/Fall/Winter
The calculus of vector fields; directional derivative, gradient, divergence, curl; potential fields; Green's, Stokes', and the divergence integral theorems. Applications in engineering and physics. Taught at the rate of seven hours per week for five weeks. Prerequisites: MA1115.
MA2025 Logic and Discrete Mathematics I (4-1) Summer/Winter
MA2025 is a first course in discrete mathematics for students of mathematics and computer science. Topics include propositional and predicate logic up to the deduction theorem, methods of mathematical proof, naive set theory, properties of functions, sequences and sums, mathematical induction, an introduction to divisibility and congruences, and an introduction to enumerative combinatorics. Prerequisites: None, although a review of algebra skills is recommended.
MA2043 Introduction to Matrix and Linear Algebra (4-0) As Required
The fundamental algebra of vectors and matrices including addition, scaling, and multiplication. Block operations with vectors and matrices. Algorithms for computing the LU (Gauss) factorization of an MxN matrix, with pivoting. Matrix representation of systems of linear equations and their solution via the LU factorization. Basic properties of determinants. Matrix inverses. Linear transformations and change of basis. The four fundamental subspaces and the fundamental theorem of linear algebra. Introduction to eigenvalues and eigenvectors. Prerequisites: Students should have mathematical background at the level generally expected of someone with a B.S. in Engineering, i.e., familiarity with Calculus and solid algebra skills. EC1010 (May be taken concurrently.)
MA2121 Differential Equations (4-0) Spring/Summer/Fall/Winter
Ordinary differential equations: linear and nonlinear (first order) equations, homogeneous and non-homogeneous equations, linear independence of solutions, power series solutions, systems of differential equations, Laplace transforms. Applications include radioactive decay, elementary mechanics, mechanical and electrical oscillators, forced oscillations and resonance. Prerequisites: MA1114.
MA2300 Mathematics for Management (5-0) Winter/Spring/Summer
Mathematical basis for modern managerial tools and techniques. Elements of functions and algebra; differential calculus of single- and multi-variable functions; integration (antidifferentiation) of single-variable functions. Applications of the derivative to rates of change, curve sketching, and optimization, including the method of Lagrange multipliers. Prerequisite: College algebra.
MA3001 Incremented Directed Study (Variable 1-0 or 2-0) (V-0) As Required
Provides the opportunity for a student who is enrolled in a 3000 level mathematics course to pursue the course material and its applications in greater depth by directed study to the extent of one additional hour beyond the normal course credit. Prerequisites: Enrollment in a 3000 level mathematics course and consent of instructor.
MA3025* Logic and Discrete Mathematics II (4-1) As Required
Provides a rigorous foundation in logic and elementary discrete mathematics to students of mathematics and computer science. Topics from logic include modeling English propositions, propositional calculus, quantification, and elementary predicate calculus. Additional mathematical topics include elements of set theory, mathematical induction, relations and functions, and elements of number theory. Prerequisites: MA2025 (preferable) or MA1025.
MA3030 Introduction to Combinatorics and Its Applications (4-1) As Required
Provides a thorough grounding in elementary combinatorics and its applications to computer science and discrete probability theory to students of computer science who concurrently take MA3025, Logic and Discrete Mathematics. Topics from combinatories include fundamental counting rules, binomial and multinomial theorems, the pigeonhole and inclusion/exclusion principles, and homogeneous recurrence relations. Elementary discrete probability is covered, up to the expectation of a discrete random variable. Corequisite: MA3025.
MA3042 Linear Algebra (4-0) As Required
Finite-dimensional vector spaces, linear dependence, basis and dimension, change of basis. Linear transformations and similarity. Scalar product, inner product spaces. Orthogonal subspaces and least squares. LU (with pivoting), Cholesky, and QR factorizations. Eigenvalues/eigenvectors, diagonalization. Hermitian matrices, quadratic forms, definite matrices. Vector and matrix norms, orthogonal transformations, condition numbers. Prerequisite: MA1114.
MA3046 Matrix Analysis (4-1) As Required
This course provides students in the engineering and physical sciences curricula with an applications-oriented coverage of major topics of matrix and linear algebra. Matrix factorizations (LU, QR, Cholesky), the Singular Value Decomposition, eigenvalues and eigenvectors, the Schur form, subspace computations, structured matrices. Understanding of practical computational issues such as stability, conditioning, complexity, and the development of practical algorithms. Prerequisites: MA2043 and EC1010.
MA3110 Intermediate Analysis (4-0) Summer/Winter
Multi-variable calculus integrated with linear algebra. Functions of several variables, continuous transformations, Jacobians, chain rule, implicit function theorem, inverse function theorem, extreme, optimization and Lagrange multiplier technique. Applications in Operations Research. Prerequisites: MA1115 and MA3042.
MA3132 Partial Differential Equations and Integral Transforms (4-0) Spring/Summer/Fall/Winter
Solution of boundary value problems by separation of variables; Sturm-Liouville problems; Fourier and Bessel series solutions, Fourier transforms; classification of second-order equations; applications, method of characteristics. Applications to engineering and physical science. Satisfies the ESR in differential equations for the Applied Mathematics program. Prerequisites: MA2121 and MA1116.
MA3139 Fourier Analysis and Partial Differential Equations (4-0) Summer/Winter
Fourier series; solution of the one and two-dimensional wave equations, D'Alembert's solution, frequency and time domain interpretations; Fourier integral transforms and applications to ordinary and partial differential equations and linear systems; Convolution theorems. Course covers basic material essential for signal processing, filtering, transmission, waveguides, and other related problems. Applications include spectral analysis of electronic signals, e.g., radar or sonar. Designed for UW and EW/IW students. Prerequisites: MA1115 and MA2121.
MA3185 Tensor Analysis (3-0) Fall
Definition and algebra of tensors. Dyadic representation in Cartesian and general components. Calculus of tensor fields in curvilinear coordinates. Derivation and application of the basic equations of heat conduction, rigid body mechanics, elasticity, fluid mechanics, electromagnetism, Newtonian and Einsteinian orbital mechanics. Prerequisites: MA1116.
MA3232 Numerical Analysis (4-0) Spring/Summer/Fall/Winter
Provides the basic numerical tools for understanding more advanced numerical methods. Topics for the course include: Sources and Analysis of Computational Error, Solution of Nonlinear Equations, Interpolation and Other Techniques for Approximating Functions, Numerical Integration and Differentiation, Numerical Solution of Initial and Boundary Value Problems in Ordinary Differential Equations, and Influences of Hardware and Software. Prerequisites: MA1115, MA2121 and ability to program in MATLAB and MAPLE.
MA3243 Numerical Methods for Partial Differential Equations (4-1) Winter
Course designed to familiarize the student with analytical techniques as well as classical finite difference techniques in the numerical solution of partial differential equations. In addition to learning applicable algorithms, the student will be required to do programming. Topics covered include: Implicit, Explicit, and Semi-Implicit methods in the solution of Elliptic and Parabolic PDE's, iterative methods for solving Elliptic PDEs (SOR, Gauss-Seidel, Jacobi), the Lax-Wendroff and Explicit methods in the solution of 1st and 2nd order Hyperbolic PDEs. Prerequisites: MA3132 and the ability to program in a high level language such as Fortran, C, or MATLAB.
MA3261 Basic Parallel Computation (3-0) As Required
The course has two goals: First, to introduce fundamental issues such as shared vs. distributed memory, connection topologies, communication algorithms, speedup, efficiency, storage requirements, granularity, pipelining, problem scaling, and useful paradigms for algorithm development. Second, to develop working proficiency by designing, implementing, and evaluating the performance of several parallel algorithms. These include, but are not limited to, numerical quadrature, matrix computations, sorting, network analysis, and dynamic programming. Prerequisites: MA1115 or MA3025 and ability to program in a high-level language.
MA3301 Linear Programming (Same as OA3201) (4-0) As Required
See OA3201 for course description.
MA3393 Topics in Applied Mathematics (V-0) As Required
A selection of topics in applied mathematics. The course content varies and the credit varies. This course is intended to reflect study for the beginning graduate student in an area for which no formal course is taught. Credit for this course may be granted more than one time to an individual student. Prerequisites: Consent of instructor.
MA3560* Applied Modern Algebra and Number Theory (4-0) As Required
This course is devoted to aspects of modern algebra and number theory that directly support applications, principally in communication. The algebraic emphasis is on ring and field theory, with special emphasis on the theory of finite fields, as well as those aspects of group theory that are important in the development of coding theory. Elements of number theory include congruences and factorization. Applications are drawn from topics of interest to DoN/DoD. These include error correcting codes and cryptography. Prerequisites: MA3025.
MA3607 Introduction to Real Analysis (4-0) Summer
The objective of this course is for students to achieve a solid understanding of the basic concepts, analysis, and proofs in advanced calculus, including: limits, sequences, series, continuous functions, uniform convergence and uniform continuity, differentiation, and Riemann integration. This is a mathematics course in the pure sense. Proofs will be emphasized, and the student will learn how to reproduce, understand, create and enjoy mathematical proofs. Prerequisites: MA1114.
MA3610 Topology, Fractals, and Chaotic Dynamics (3-0) As Required
An introductory course on chaotic dynamics systems and fractals. Topics covered include: flows on the line, bifurcations, linear systems, phase plane, limit cycles, the Lorenz equations, fractals, and one-dimensional maps. Applications include population growth, laser threshold, the pendulum, relaxation oscillations, and synchronized chaos. Prerequisites: MA1115 and MA2121.
MA3677 Theory of Functions of a Complex Variable I (4-0) As Required
Selected topics from the theory of functions of a complex variable; analytic functions, power series, Laurent series. Singularities of analytic functions; contour integration and residues; applications of residues to real integrals and Laplace transforms, zeros of analytic functions, infinite product representation for analytic functions; maximum modulus theorems for analytic and harmonic functions; conformal mapping. Applications include interference effects in optics and problems from heat flow and fluid flow. Prerequisites: MA1115.
MA3730 Theory of Numerical Computation (3-0) As Required
Analysis of computational methods used for the solution of problems from the areas of algebraic equations, polynomial approximation, numerical differentiation and integration, and numerical solutions of ordinary differential equations. Prerequisites: MA2121.
MA4026 Combinatorial Mathematics (4-0) As Required
Advanced techniques in enumerative combinatorics and an introduction to combinatorial structures. Topics include generating functions, recurrence relations, elements of Ramsey theory, theorems of Burnside and Polya, and balanced incomplete block designs. Application areas with DoD/DoN relevance range from mathematics to computer science and operations research, including applications in probability, game theory, network design, coding theory, and experimental design. Prerequisites: MA3025.
MA4027 Graph Theory and Applications (4-0) As Required
Advanced topics in the theory of graphs and digraphs. Topics include graph coloring, Eulerian and Hamiltonian graphs, perfect graphs, matching and covering, tournaments, and networks. Application areas with DoD/DoN relevance range from mathematics to computer science and operations research, including applications to coding theory, searching and sorting, resource allocation, and network design. Prerequisites: MA3025.
MA4103 Thesis Topics Seminar (3-0) As Required
Explores in depth discrete dynamical systems and the thesis topics of students enrolled in the Applied Mathematics degree program. Fulfills the ESR to provide students with the experience of organizing and presenting applied mathematical ideas to students and faculty, including a classroom environment. Prerequisites: Consent of instructor. Graded on a Pass/Fail basis only.
MA4237 Advanced Topics in Numerical Analysis (V-0) Fall
The subject matter will vary according to the abilities and interest of those enrolled. Applications of the subject matter to DoD/DoN are discussed. Prerequisites: Consent of instructor.
MA4242 Numerical Solution of Ordinary Differential Equations (3-1) As Required
Adams formulas, Runge-Kutta formulas, extrapolation methods, implicit formulas for stiff equations; convergence and stability, error estimation and control, order and stepsize selection, applications. Prerequisites: MA3232.
MA4243 Numerical Solution of Partial Differential Equations (3-1) As Required
Finite difference methods for parabolic, elliptic, and hyperbolic equations, multi-grid methods; convergence and stability, error estimation and control, numerical solution of finite difference equations, applications. Prerequisites: MA3132, MA3232 suggested.
MA4245 Mathematics Foundation of Galerkin Methods (4-0) As Required
Variational formulation of boundary value problems, finite element and boundary element approximations, types of elements, stability, eigenvalue problems. Prerequisites: MA3132, MA3232 or equivalent.
MA4248 Computational Linear Algebra (4-1) As Required
Development of algorithms for matrix computations. Rounding errors and introduction to stability analysis. Stable algorithms for solving systems of linear equations, linear least squares problems and eigen problems. Iterative methods for linear systems. Structured problems from applications in various disciplines. Prerequisites: MA3046, or consent of instructor, advanced MATLAB programming.
MA4261 Distributed Scientific Computing (3-2) As Required
General principles of parallel computing, parallel techniques and algorithms, solution of systems of linear equations, eigenvalues and singular value decomposition, domain decomposition and application (e.g., satellite orbit determination and shallow water fluid flow). Prerequisites: MA3042 or MA3046, MA3132, and MA3232.
MA4301 Nonlinear Programming (Course Taught by or Staff, Same as OA4201) (4-0) As Required
See OA4201 for course description.
MA4302 Design of Experiments (Course Taught by or Staff, Same as OA4101) (3-1) As Required
See OA4101 for course description.
MA4303 Regression Analysis (Course Taught by or Staff, Same as OA4102) (4-0) As Required
See OA4102 for course description.
MA4304 Time Series Analysis (Course Taught by or Staff, Same as OA4308) (4-0) As Required
See OA4308 for course description.
MA4305 Scholastic Models II (Course Taught by or Staff, Same as OA4301) (4-0) As Required
See OA4301 for course description.
MA4311 Calculus of Variations (3-0) As Required
Euler equation, Weierstrass condition, Legendre condition, numerical procedures for determining solutions, gradient method, Newton method, Transversability condition, Rayleigh Ritz method, conjugate points. Concepts are related to geometric principles whenever possible. Prerequisites: MA2121 (programming experience desirable).
MA4321 Stability, Bifurcation and Chaos (3-0) As Required
Differential equations and dynamical systems, equilibrium of autonomous systems, stability, Liapunov's method, examples of chaos, local bifurcations of vector fields and maps, chaotic dynamical systems. Prerequisites: MA3610.
MA4322 Principles and Techniques of Applied Mathematics I (4-0) As Required
Selected topics from applied mathematics to include: Dimensional Analysis, Scaling, Stability and Bifurcation, Perturbation Methods— regular and singular with boundary layer analysis, as well as, asymptotic expansions of integral, integrals equations, Green's functions of boundary value problems, and distribution theory. Prerequisites: MA3042 and MA3132; MA3232 strongly recommended.
MA4323 Principles and Techniques of Applied Mathematics II (4-0) As Required
Continuation of MA4322. Selected topics include: calculus of variations, Hamiltonian Mechanics, distribution theory and Green's Functions in two and three dimensions, and discrete models. Prerequisites: MA4322
MA4332 Partial Differential Equations (4-0) As Required
This course provides an introduction to the theory of partial differential equations. It includes the following topics: classification of second order equations; initial value and boundary value problems for hyperbolic, parabolic, and elliptic partial differential equations; existence and uniqueness of linear elliptic and parabolic PDEs; nonlinearparabolic and elliptic PDEs; Hamilton-Jacobi equations; systems of conservation laws and nonlinear wave equations; transform methods and Green's functions. Prerequisites: MA3132, and MA3232 strongly recommended.
MA4362 Astrodynamics (3-0) As Required
Review of the two-body problem. The effects of a third point mass and a distributed mass. Expansion of the disturbing potential in series of Legendre functions. Variation of parameter equations for osculating orbital elements. Perturbation and numerical solution techniques. Statistical orbit determination. Codes used by the military to maintain the catalog of artificial satellites and space debris. Prerequisites: SS3500 or equivalent.
MA4372 Integral Transforms (3-0) As Required
The Laplace, Fourier and Hankel transforms and their inversions; Asymptotic behavior. Applications to problems in engineering and physics. Prerequisites: MA3132.
MA4377 Asymptotic and Perturbation Methods I (3-0) As Required
Advanced course in the application of approximate methods to the study of integrals and differential equations arising in physical problems. Topics covered include: asymptotic sequences and expansions, integrals of a real variable, contour integrals, limit process expansions applied to ordinary differential equations, multiple variable expansion procedures and applications to partial differential equations. Prerequisites: MA3132.
MA4378 Asymptotic and Perturbation Methods Ii (3-0) As Required
Continuation of MA4377. Prerequisites: MA4377.
MA4391 Analytical Methods for Fluid Dynamics (4-0) As Required
The basic fluid dynamic equations will be derived, and a variety of analytical methods will be applied to problems in viscous flow, potential flow, boundary layers, and turbulence. Applications in aeronautics will be discussed. Prerequisites: MA3132 or MA3139.
MA4392 Numerical Methods for Fluid Dynamics (4-0) As Required
Numerical methods exclusively will be applied to fluid dynamics problems in viscous flow, potential flow, boundary layers, and turbulence. Applications in aeronautics will be discussed. Prerequisites: MA3232 and MA4391.
MA4393 Topics in Applied Mathematics (V-0) Fall
The course content varies but applications of interest to the DoN/DoD will be discussed. Credit may be granted for taking this course more than once. Prerequisites: Consent of instructor.
MA4400 Cooperation and Competition (4-0) As Required
The course will develop game theoretic concepts in evaluations of the importance of players in bargaining situations and of elements in networks. Topics covered include cooperative and noncooperative games, bargaining, the Shapley Value, and coalitions. The course will study applications to military problems and applications to economics, political science, and biology. There will be extensive reading from the literature. Prerequisites: MA3042, OA3201, and an introductory course in probability.
MA4450 Combinatorial and Cryptographic Properties of Boolean Functions (4-0) As Required
The course will discuss the Fourier analysis of Boolean functions and the relevant combinatorics with an eye toward cryptography and coding theory. Particular topics will include avalanche features of Boolean functions, correlation immunity and resiliency, bentness, trade-offs among cryptographic criteria and real-life applications in the designs of stream and block ciphers. Prerequisite: MA3025 or a similar combinatorial/discrete mathematics course (and recommended, but not required, an introductory course in probability).
MA4560* Coding and Information Theory (4-0) As Required
Mathematical analysis of the codes used over communication channels is made. Techniques developed for efficient, reliable and secure communication are stressed. Effects of noise on information transmission are analyzed and techniques to combat their effects are developed. Linear codes, finite fields, single and multiple error-correcting codes are discussed. Codes have numerous applications for communication in the military, and these will be addressed. Prerequisites: MA3560.
MA4565 Advanced Modern Algebra (3-0) As Required
A continuation of MA3560. Rings, ring homomorphism, integral domains and Euclidean domains. Unique factorization rings, polynomial rings. Modules and ideals. Noetherian rings, Field extension and Galois theory. Prerequisites: MA3560.
MA4570 Cryptography (4-0) As Required*
The methods of secret communication are addressed. Simple cryptosystems are described and classical techniques of substitution and transposition are considered. The public-key cryptosystems, RSA, Discrete Logarithm and other schemes are introduced. Applications of cryptography and cryptanalysis. Prerequisites: MA3560.
MA4593 Topics in Algebra (3-0) Fall
A selection of topics in algebra. Content of the course varies. Credit for taking the course more than once is allowed. Students may select a topic of interest to the DoN/DoD, so the course can support the MERs in a variety of curricula. Prerequisite: MA3560.
MA4620 Theory of Dynamical Systems (4-0) As Required
This course provides an introduction to the theory of dynamical systems providing a basis for the analysis and design of systems in engineering and applied science. It includes the following topics: Second order linear systems; contraction mapping, existence and uniqueness of solutions; continuous dependence on initial conditions; comparison principle; Lyapunov stability theorems; LaSalle's theorem; linearization methods; nonautonomous systems; converse theorems; center manifold theorems; and stationary bifurcations of nonlinear systems. Prerequisites: MA2121 and MA3042.
MA4635 Functions of Real Variables I (3-0) As Required
Semi-continuous functions, absolutely continuous functions, functions of bounded variation; classical Lebesgue measure and integration theory, convergence theorems and Lp spaces. Abstract measure and integration theory, signed measures, Radon-Nikodym theorem; Lebesgue decomposition and product measure; Daniell integrals and integral representation of linear functionals. Prerequisites: MA3606.
MA4636 Functions of Real Variables II (3-0) As Required
Continuation of MA4635. Prerequisites: MA4635.
MA4675 Complex Analysis (4-0) As Required
A continuation of MA3677. Differential equations in the complex plane, transform methods, the Wiener-Hopf method, integral equations, discrete Fourier analysis. Prerequisite: MA3677.
MA4693 Topics in Analysis (3-0) Spring
Content of the course varies. Students will be allowed credit for taking the course more than once. Prerequisites: Consent of instructor.
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MO designated courses are intended for students in operational curricula only. They do not satisfy the mathematics course requirements for accredited engineering curricula, nor do they satisfy the prerequisites for any of the MA designated courses.
MO1180 Topics in Mathematics for Systems Analysis (3-2) Spring/Fall
A one quarter course in logic, elementary mathematics, combinatorics, and matrix algebra, plus a review of selected topics from single variable calculus with extensions to two variables. This course is intended for first-quarter students in the distributed learning Master of Systems Analysis curriculum. Logic places emphasis on the Propositional and Predicate Calculus. Elementary mathematical topics include sets, functions, and relations. Coverage of combinatorics includes an introduction to basic principles of counting (sum and product rules), permutations, and combinations. The fundamental algebra of matrices includes addition, multiplication of matrices, and multiplication of a matrix by a constant, and a column (vector) by a matrix; elementary matrices and inverses, together with the properties of these operations; solutions to m x n systems of linear algebraic equations using Gaussian elimination. Selected topics from single-variable calculus are extended to functions of two-variables, including double integrals over rectangles and general regions. (This course may not be taken for credit by students in an engineering or science degree program, nor may it be used as a prerequisite for any other mathematics course). Prerequisite: Single-variable calculus.
MO1901 Mathematics for ISSO (3-0) As Required
A brief survey of selected calculus and post-calculus topics—single variable derivatives and integrals, infinite series and sequences, complex numbers, and Fourier series and transforms. (This course may not be taken for credit by students in an engineering or science degree program, nor may it be used as a prerequisite for any other mathematics course.) Prerequisites: None.
MO1903 Mathematics for ISSO Space Systems Operations Specialization (3-0) Fall
To be taken concurrently with MA1114. The course consists of a brief survey of the following topics: Complex numbers, Fourier series and transforms, and Ordinary Linear Differential Equations. (This course may not be taken for credit by students in an engineering or science degree program, nor may it be used as a prerequisite for any other mathematics course.) Taught at the rate of seven hours per week for five weeks. Prerequisites: MA1113.
*Required courses for the certificate program Mathematics of Secure Communication.
Program Officer
Kendrick Macklin, LCDR
Code 73, Spanagel Hall, Room 401A
Academic Associate
Bard Mansager
Code MA, Spanagel Hall, Room 248B
(831) 656-2295, DSN 878-2695, FAX (831) 656-2355
Brief Overview
This program is designed to meet the needs of the Department of Defense for graduates who are skilled in applying concepts of higher mathematics. The objective of the program is to equip an officer with the skill to analyze a military problem, formulate it in mathematical terms, solve or approximate a solution, and interpret and present the results.
Completion of this curriculum also qualifies an officer as an Applied Mathematics Subspecialty with a code of 4100P. A typical job in this subspecialty is an instructor in mathematics at the U.S. Naval Academy or the U.S. Military Academy at West Point.
Requirements for Entry
Preparatory to graduate work in applied mathematics, the officer shall have completed a strong program of study at the undergraduate level or the first three quarters of the mathematics core sequence, which includes linear algebra, advanced calculus in one and several variables, ordinary differential equations, probability and statistics. Officers not having the required qualifications for direct input enter the program indirectly through the Engineering Science (460) curriculum. An APC of 324 is required.
Entry Date
Advanced Science (Applied Mathematics) is an eight-quarter course of study with preferred entry date in June. If further information is needed, contact the Academic Associate or Program Officer for this curriculum.
Typical Course of Study
Quarter 1
(4-0) |
Single Variable Calculus I |
|
(4-0) |
Single Variable Calculus II w/ Matrix Algebra |
|
(4-0) |
Logic & Discrete Mathematics I |
|
(4-2) |
Strategy & Policy |
Quarter 2
(4-0) |
Multi-variable Calculus |
|
(3-0) |
Vector Calculus |
|
(4-1) |
Logic & Discrete Mathematics II |
|
(4-0) |
Linear Algebra |
Quarter 3
(4-0) |
Linear Algebra |
|
(4-0) |
Intermediate Analysis |
|
(4-0) |
Differential Equations |
|
(3-0) |
Modern Appl Algebra $ Num Theory |
|
|
|
|
Quarter 4
(4-0) |
Joint Maritime Ops I |
|
(4-0) |
Linear Programming |
|
(4-0) |
PDEs |
|
(4-1) |
Probability |
Quarter 5
(-0) |
Joint Maritime Ops II |
|
(4-0) |
Real Analysis |
|
(4-0) |
Num Analysis |
|
(4-1) |
Statistics |
Quarter 6
(4-0) |
Principles and Techniques of Applied Mathematics I |
|
(4-0) |
Complex Analysis |
|
MA3xxx |
(3-0) |
Elective |
(4-1) |
Data Analysis |
Quarter 7
(4-0) |
Principles and Techniques of Applied Mathematics II |
|
(4-0) |
Theses Research |
|
MA4xxx |
(3-0) |
Elective |
MA4xxx |
(4-0) |
Elective |
Quarter 8
(4) |
Thesis Research |
|
(4) |
Thesis Research |
|
MA4xxx |
(3-0) |
Elective |
(4-0) |
National Security Decision |
Educational Skill Requirements (ESR)
Applied Mathematics - Curriculum 380
The value of graduate education in mathematics lies in the vast breadth of its applicability. The officer with advanced education in mathematics possesses skills in problem solving, modeling, abstraction, optimization, and analysis that are sufficiently general that they apply in many arenas and never lose their currency in the face of changing technology and yet-to-be-identified needs. Graduate education in mathematics is a career-long enabler. Students in the Applied Mathematics curriculum will receive a solid mathematical foundation as they transition into graduate curricula emphasizing relevant and modern advanced mathematical techniques. Students will be encouraged to develop and utilize skills in analysis, reasoning, creativity, and exposition as they acquire knowledge of mathematics and its applications.
1. Fundamental Areas: The officer will complete courses in the following fundamental areas of Mathematics, developing sufficient mastery to qualify for teaching Mathematics at the undergraduate level.
2. Applications: The officer will become well-versed in the applications of mathematics to real world problems of interest to the military, enhancing performance in post-graduate operational billets and policy making positions.
3. Computer Skills: The officer will acquire the ability to use higher-level structured computer languages on current workstations
4. Communication and Research Skills: The officer will perform independent research in an area of Mathematics, develop written and oral presentation skills, and gain instructional experience.
5. Joint Professional Military Education: Graduates will complete the Navy Joint Professional Military Education Phase I requirements.
Academic Associate
Senior Lecturer Bard Mansager
Code MA/Ma, Spanagel Hall, Room 248B
(831) 656-2695, DSN 756-2695, FAX (831) 656-2355
Brief Overview
The Mathematics of Secure Communication certificate program comprises four upper division and graduate level courses. Upon successful completion of the coursework, students will be awarded a certificate of accomplishment, in keeping with standard practices of the Naval Postgraduate School. The purpose of this program is to provide mathematics education to naval officers and DoD civilians in the broad areas of Cryptography, Coding and Information Theory, and Secure Communications.
Requirements for Entry
Requirements for entry include completion of an introductory course in Discrete Mathematics equivalent to MA2025. Also required is a baccalaureate degree with an academic profile code (APC) of 324.
Entry Dates
At the beginning of the spring and fall quarters, with start dates in late March/ early April and late September/ early October, respectively.
Program Length
Four quarters.
Graduation Requirements
Requirements for the graduate certificate in Mathematics of Secure Communication are met by successful completion of all four courses.
Required Courses
Quarter 1
(4-1) |
Logic and Discrete Mathematics II |
Quarter 2
(4-0) |
Applied Modern Algebra and Number Theory |
Quarter 3
(4-0) |
Coding and Information Theory |
Quarter 4
(4-0) |
Cryptography |
Chairman
Jeffrey Knorr, Ph.D.
Code EC, Spanagel Hall, Room 437A
(831) 656-2081, DSN 756-2081, FAX (831) 656-2760
Associate Chairman, Instruction
R. Clark Robertson, Ph.D.
Code EC/Rc, Spanagel Hall
Room 414A
(831) 656-2383, DSN 756-2383
Associate Chairman, Student Programs
Monique P. Fargues, Ph.D.
Code EC/Fa, Spanagel Hall
Room 456
(831) 656-2859, DSN 756-2859
Associate Chairman, Research
Murali Tummala, Ph.D.
Code EC/Tu, Spanagel Hall
Room 448B
(831) 656-2645, DSN 756-2645
Richard W. Adler, Research Associate Professor (1970)*; Ph.D., Pennsylvania State University, 1970.
Robert W. Ashton, Associate Professor (1992); Ph.D., Worcester Polytechnic Institute, 1991.
Jon T. Butler, Professor (1987); Ph.D., Ohio State University, 1973.
Roberto Cristi, Professor (1985); Ph.D., University of Massachusetts, 1983.
Monique P. Fargues, Associate Professor and Associate Chair for Student Programs (1989); Ph.D., Virginia Polytechnic Institute and State University, 1988.
Douglas J. Fouts, Professor (1990); Ph.D., University of California at Santa Barbara, 1990.
Tri T. Ha, Professor (1987); Ph.D., University of Maryland, 1977.
Timothy Hobbs, CDR, USN, Military Instructor and Program Officer (2002); MSEE, Naval Postgraduate School, 1990.
Robert (Gary) Hutchins, Associate Professor (1993); Ph.D., University of California at San Diego, 1988.
David C. Jenn, Professor (1990); Ph.D., University of Southern California, 1989.
Alex Julian, Assistant Professor (2004); Ph.D., University of Wisconsin, Madison, 1997.
Jeffrey B. Knorr, Professor and Chair (1970); Ph.D., Cornell University, 1970.
Frank Kragh, Assistant Professor (2003); Ph.D., Naval Postgraduate School, 1997.
Herschel H. Loomis, Jr., Professor (1981); Ph.D., Massachusetts Institute of Technology, 1963.
John McEachen, Associate Professor (1996); Ph.D., Yale University, 1995.
Sherif Michael, Professor (1983); Ph.D., University of West Virginia, 1983.
Michael A. Morgan, Professor (1979); Ph.D., University of California at Berkeley, 1976.
Phillip E. Pace, Professor (1992); Ph.D., University of Cincinnati, 1990.
Andrew Parker, Research Associate (1996); M.S., University of Maryland, 1994; MSES, Naval Postgraduate School, 1992
John P. Powers, Distinguished Professor (1970); Ph.D., University of California at Santa Barbara, 1970.
R. Clark Robertson, Professor and Associate Chair for Instruction (1989); Ph.D., University of Texas at Austin, 1983.
Weilian Su, Assistant Professor (2004); Ph.D., Georgia Institute of Technology, 2004.
Frederick Terman, Senior Lecturer (1983); MSEE, Stanford University, 1964.
Charles W. Therrien, Professor (1984); Ph.D., Massachusetts Institute of Technology, 1969.
Murali Tummala, Professor and Associate Chair for Research (1987); Ph.D., India Institute of Technology, 1984.
W. Ray Vincent, Research Associate Professor (1980); M.S., Michigan State University, 1948.
Donald van Z. Wadsworth, Senior Lecturer (1988); Ph.D., Massachusetts Institute of Technology, 1958.
Todd Weatherford, Associate Professor (1995); Ph.D., North Carolina State University, 1993.
Lonnie Wilson, Research Associate Professor (1997); Ph.D., University of California at Los Angeles, 1973.
Xiaoping Yun, Professor (1994); Sc.D., Washington University, 1987.
Lawrence J. Ziomek, Professor (1982); Ph.D., Pennsylvania State University, 1981.
*The year of joining the Naval Postgraduate School faculty is indicated in parentheses.
Brief Overview
The Department of Electrical and Computer Engineering is the major contributor to programs for the education of officers in the Electronic Systems Engineering curriculum, the Combat Systems curriculum, and the Space Systems Engineering curriculum. Additionally, the department offers courses in support of other curricula such as Information Warfare/Electronic Warfare; Information Technology Management; Command, Control, Communications, Computers and Intelligence (C4I); Space Systems Operations; Underwater Acoustics and Engineering Acoustics.
The program leading to the MSEE is accredited as an Electrical Engineering Program at the advanced level by the Engineering Accreditation Commission of ABET, 111 Market Place, Suite 1050, Baltimore, MD 21202-4012 - telephone: (410) 347-7700.
If needed, an MSEE student will usually spend six to twelve months learning or reviewing material at a junior or senior level before entering into graduate studies. The graduate study portion of a typical program is about one year in duration with a combination of course study and thesis work being performed. The thesis portion of the study is the equivalent of four courses with an acceptable written thesis being a requirement for graduation.
The curriculum is organized to provide the students with coursework spanning the breadth of Electrical and Computer Engineering. In addition, students concentrate in one major area of Electrical and Computer Engineering by taking a planned sequence of advanced courses. Currently there are formal concentrations in:
Communications Systems
Computer Systems
Guidance, Navigation and Control Systems
Joint Services Electronic Warfare (International students only)
Network Engineering Sensor Systems
Power Systems and Microelectronics
Signal Processing Systems
Network Engineering
Sensor Systems
The department has about thirty-two faculty members, either on a permanent or visiting basis, contributing to the instructional and research programs.
Mission
The ECE department seeks to provide NPS students with the highest quality and most DoD-relevant graduate education available in electrical and computer engineering.
Degree
The department offers programs leading to the Master of Science degree in Electrical Engineering (MSEE), the Master of Science in Engineering Science with a major in Electrical Engineering [MSES(EE)], the degree of Electrical Engineer (EE) and Doctor of Philosophy (Ph.D.). A student is able to earn an academic degree listed above while enrolled in Electronic Systems Engineering (Curriculum 590), Electrical Engineering (Curriculum 590), Space Systems Engineering (Curriculum 591), Combat Systems Science & Technology (Curriculum 533), and Undersea Warfare (Curriculum 525). The department typically graduates over forty MSEE degree candidates, one EE degree recipient and three Ph.D.s per year.
A Bachelor of Science in Electrical Engineering or its equivalent is required. Credits earned at the Naval Postgraduate School and credits from the validation of appropriate courses at other institutions are combined to achieve the degree equivalence.
To complete the course requirements for the master's degree, a student needs a minimum of 52 credit hours of graduate level work. There must be a minimum of 36 credits in the course sequence 3000 - 4999, of which at least 30 credits must be in Electrical and Computer Engineering. The remainder of these 36 credits must be in engineering, mathematics, physical science, and/or computer science. Specific courses may be required by the department and at least four courses that total a minimum of 12 credits, must be in the course sequence 4000 - 4999.
An acceptable thesis for a minimum of 16 credits must be presented to, and approved by, the department.
MSEE Program Objectives: The MSEE program has the following objectives (i.e., skills and abilities that graduates can bring to their position after having graduated from NPS and receiving 3-5 more years of on-the-job training and professional development):
MSEE Program Outcomes: In order to achieve the above objectives, we expect to provide the student with a program with the following attributes upon completion of their program.
Students with acceptable academic backgrounds may enter a program leading to the degree Master of Science in Engineering Science with an emphasis in Electrical Engineering [MSES{EE} degree]. The program of each student seeking this degree must contain at least 52 credit hours of graduate level work including 36 credit hours in the course sequence 3000 - 4000. Of these 36 course credits, at least 20 must be in Electrical and Computer Engineering, and an additional 12 must be in engineering, mathematics, physical science and/or computer science. At least 12 of the 36 must be in the course sequence 4000-4999. All students must submit an acceptable thesis of at least 16 credit hours. This program provides depth and diversity through specially arranged course sequences to meet the needs of the Navy and the interests of the individual. The department chairman's approval is required for all programs leading to this degree.
Students with strong academic backgrounds may enter a program leading to the degree of Electrical Engineer.
A minimum of 96 total graduate credits is required for the award of the engineer's degree, of which at least 24 must be in accepted thesis research, and at least 54 credits must be in Electrical and Computer Engineering courses.
At least 36 of the total hours are to be in courses in the sequence 4000 - 4999. Approval of all programs must be obtained from the Chairman, Department of Electrical and Computer Engineering.
The Total Ship Systems Engineering Program is an interdisciplinary, systems engineering and design-oriented program available to students enrolled in Mechanical Engineering, Electrical and Computer Engineering or Combat Systems programs. The program objective is to provide a broad-based, design-oriented education focusing on the warship as a total engineering system. The eight-course sequence of electives introduces the student to the integration procedures and tools used to develop highly complex systems such as Navy ships. The program culminates in a team-performed design of a Navy ship, with students from all three curricula as team members. Students enrolled in programs leading to the Engineer Degree are also eligible for participation. Entry requirements are a baccalaureate degree in an engineering discipline with a demonstrated capability to perform satisfactorily at the graduate level. The appropriate degree thesis requirements must be met, but theses that address system design issues are welcome.
The Department of Electrical and Computer Engineering has an active program leading to the Doctor of Philosophy degree. Joint programs with other departments are possible. A noteworthy feature of these programs is that the student's research may be conducted away from the Naval Postgraduate School in a cooperating laboratory or other installation of the federal government. The degree requirements are as outlined under the general school requirements for the doctor's degree.
The laboratories of the department serve the dual role of supporting the instructional and research activities of the department. The department has well-developed laboratories in each specialty area.
Micro-electronics Lab
This lab supports design and analysis of semiconductor devices, design and development of VLSI integrated circuits, and design, implementation and testing of microprocessor and VLSI systems. Major equipment of the lab includes: Semiconductor Parameterization Equipment, Capacitance-Voltage measurement equipment, Semi-automatic Probing station, High Speed Sampling Scopes, Logic Analyzers, Printed Circuit Assembly tools, Unix and PC workstations, Silvaco(TM) TCAD simulation tools, Tanner and Cadence Design tools and Semiconductor Parameterization Equipment (high power capability), Manual Probing stations (2+), Wire-bonding equipment, and PC workstations. The lab also runs a Flash X-ray facility and a Linear accelerator (LINAC) facility for testing electronic devices.
Circuits, Signals, and Digital Systems Lab
This laboratory provides support for instruction and research in the areas of basic analog and digital logic design, discrete component testing, fundamental circuit design, micro-processing interfacing, assembly language programming and communication theory. The laboratory is equipped with micro-processing development systems including an HP64000 for advanced course work and thesis research, CAD facilities capable of schematic capture, circuit simulation, and fault detection. The lab utilizes various test equipment to include, but not limited to, oscilloscopes, signal generators, spectrum analyzers, multi-meters, and high-speed data acquisition equipment.
Academic Computing Lab
This laboratory is the primary computational facility within the Department of Electrical and Computer Engineering and incorporates PC/Windows, PC/Linux, and Sun/Solaris workstations. Various high-performance computing platforms are also available, such as a SRC Computers model SRC-6e, which has a reconfigurable processor architecture. The laboratory also includes a secure computing facility for classified computing up to the Secret level on PCs, workstations, and a high-performance Linux cluster. The Academic Computing Laboratory is first and foremost a teaching facility for accomplishing computer assignments that are assigned as a part of ECE courses. It is used for research-related computing only when such computing does not interfere with course work. Typically, this is accomplished by reserving workstations for specific times when courses meet and by running research-related programs at lower priority levels. The laboratory serves approximately 350 students annually and supports over 25 courses and over 12 curriculums. The software installed on the servers in this laboratory are engineering design, analysis, and simulation tools related to the disciplines of Electrical and Computer Engineering, such as OPNET for network design and simulation, PSPICE and SmartSPICE for circuit design and simulation, and the entire suite of software from Silvaco International for modeling and simulating solid state devices, virtual wafer fabrication, and the design, modeling, and simulation of analog, digital, and mixed-signal integrated circuits.
Optical Electronics Lab
This laboratory provides educational and research support in the areas of fiber optics, lasers, and electro-optics. The laboratory has a variety of fiber optics instrumentation (including two OTDRs, a fusion splicer, optical spectrum analyzer, connector application equipment, a 1.5 Gb/s digital pattern generator and BER tester, an optical fiber amplifier, optical autocorrelator for pulse width measurement, various diode laser controllers), RF and microwave instrumentation (signal synthesizer, microwave spectrum analyzer), and general-purpose test instrumentation. Various detectors and imaging equipment is also available.
Electromagnetics Lab
This laboratory supports instruction and research in the area of microwave systems and technology. This is accomplished with a mix of hardware, instruments, test systems, and software. Included in the lab inventory are scalar and vector microwave network analyzers, electromagnetic software for simulating antennas, ships and aircraft, and a software design system for simulation of microwave circuits and systems. There is also a fully automated anechoic chamber for antenna pattern measurements.
Radar and Electronic Warfare Systems Lab
The objective of the Radar and Electronic Warfare (EW) Systems Laboratory is to educate military officers and civilians in the technology and operational characteristics of electronic warfare. The Radar and Electronic Warfare Systems Laboratory supports both research and teaching. The hardware laboratory contains instrumented radar and electronic warfare equipment and has been in operation for over 35 years. Each radar system is well instrumented to operate as a teaching tool. The equipment allows the student to experience hands-on knowledge of performance characteristics, conduct experimental research, and reinforces concepts that are taught in the classroom.
Controls and Robotics Lab
This laboratory is mainly an instructional lab that supports experiments for all courses in Guidance, Navigation, Controls, and Robotics. Lab facilities include servo control stations and associated computers (equipped with A/D and D/A data acquisition cards, LabView, and Matlab/SIMULINK software) that are used to conduct simulations and physical experiments, modeling, analysis, and design of control systems. The lab is also equipped with advanced robots to support robotics laboratory assignments and thesis projects in robotics.
Power Systems Lab
The Power Systems Laboratory supports postgraduate education and thesis research related to the design, analysis, simulation and implementation of power converter and electric drive technology. Thesis research projects are closely coupled to current Department of Defense priorities including more-survivable power system architectures such as DC Zonal Electric Distribution, Integrated Power Systems, and electric propulsion. In coursework and projects, students employ modern device technologies, hardware-in-the-loop synthesis tools, simulation packages, measurement devices, and power converter and electric machine modules to assess component operation, develop feedback controls, and study evolving power system challenges. An emphasis is placed on prototyping and validating against detailed simulation models.
Digital Signal Processing Lab
This laboratory supports instruction and research in the area of Digital Signal Processing. Research and thesis work include, or have included, work in acoustic data modeling and processing, image analysis and modeling, signal detection and classification, multirate processing, target tracking, and other areas. Lab facilities include several Windows NT-based workstations, including eight workstations equipped with TI DSP boards for real-time processing, and a number of SUN workstations, including Ultra-10 and Ultra-60 for Unix-based activities.
Computer Communications and Networking Lab
This laboratory supports instruction and research in the area of network design, engineering, and infrastructure development. Thesis work and research undertaken include modeling and simulation of high-speed and wireless networks and related protocols, video transmission over ATM networks, traffic modeling, simulation and analysis, design and simulation of wide area networks, and related areas. Lab facilities include ATM switches, routers, LAN switches, video processing equipment, a channel simulator, a protocol analyzer, network simulation packages, and NT workstations.
Other support facilities within the department include the Calibration and Instrument Repair Laboratory. Classified instruction and research are supported by appropriately certified facilities.
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EC0810 Thesis Research (0-8) Spring/Summer/Fall/Winter
Every student conducting thesis research will enroll in this course. Prerequisites: None.
EC0950 Seminar (No Credit) (0-1) As Required
Lectures on subjects of current interest will be presented by invited guests from other universities, government laboratories, and from industry, as well as by faculty members of the Naval Postgraduate School. Prerequisites: None.
EC1010 Introduction to Matlab (1-1) Spring/Summer/Fall/Winter
An introductory course for students with little or no programming background using MATLAB. Basic concepts of the MATLAB environment are considered, such as matrix operations, vector and matrix manipulations, equation solving, simulation, programming, and graphing. This course prepares students for using MATLAB in future course work in the ECE department. Graded on a Pass/Fail basis only. Prerequisites: None.
EC2010 Probabilistic Analysis of Signals and Systems (3-1) Summer/Winter
The foundations of signals and systems are developed from probabilistic and statistical approaches. Emphasis is on signal processing, communication systems, and computer networks relevant to military applications. Topics include probability, random variables, and random sequences; density and distribution functions; deterministic versus nondeterministic signals; expectation, the dc and the r.m.s. values of nondeterministic signals, correlation and covariance; radar and sonar signal detection; LTI systems, transformation of random variables and the central limit theorem; basic queuing theory and computer communication networks. Prerequisites: EC2410 (may be taken concurrently).
EC2100 Circuit Analysis (3-2) Summer/Winter
The fundamental circuit analysis course for Electrical Engineering majors. The course considers circuit principles, circuit topology, direct current circuits, natural response, forced response, total response, impedance concepts, the application of the Laplace transformation to solve circuit problems and device transfer functions. The laboratories will utilize both computer software and hands-on exercises. Prerequisites: PH1322, MA2043 and MA2121 (may be concurrent).
EC2110 Circuit Analysis II (3-2) Spring/Fall
A continuation of EC2100. The course considers circuit principles, impedance concepts and steady-state ac circuits, ac power, frequency response and selectivity, basics of operational amplifiers and an introduction to machines and power converters. Prerequisites: EC2100.
EC2200 Introduction to Electronics Engineering (3-3) Summer/Winter
An introduction to electronic devices and circuits. Solid state physics and semiconductor fundamentals. Properties of p-n junctions in diodes; Bipolar Junction Transistors (BJT) and Field Effect Transistors (FET); static and dynamic models for these devices, and their linear and nonlinear applications. Applications of transistors in the design of amplifiers and digital systems. Ideal operational amplifiers characteristics and applications. Fabrication and the design of integrated circuits. Prerequisites: EC2110.
EC2220 Electrical Engineering Design (3-4) Spring
A team-based capstone engineering design course emphasizing the application of electrical engineering principles, devices, and circuits to the design, analysis, implementation, and testing of electronic systems. The intensive laboratory component initially reviews various electronic circuits useful in the design of the final project. Final projects require the design, analysis, implementation, testing and demonstration of an electronic system that also incorporates realistic parameters impacting the design process, such as economics, ergonomics, ethics, environmental impact, safety, etc. Prerequisites: EC2200.
EC2300 Control Systems (3-2) Summer/Winter
The main subject of this course is the analysis of feedback systems using basic principles in the frequency domain (Bode plots) and in the s-domain (root locus). Performance criteria in the time domain, such as steady-state accuracy, transient response specifications, and in the frequency domain such as bandwidth and disturbance rejection, will be introduced. Simple design applications using root locus and Bode plot techniques will be addressed in the course. Laboratory experiments are designed to expose the students to testing and evaluating mathematical models of physical systems using computer simulations and hardware implementations. Prerequisites: EC2100 and ability to program in MATLAB.
EC2320 Linear Systems (3-1) Spring/Fall
Formulation of system models including state equations, transfer functions, and system diagrams for continuous and sampled-data systems. Computer and analytical solution of system equations. Stability, controllability, and observability are defined. Introduction to design by pole placement using measured and estimated state feedback. Application to military systems is introduced via example. Prerequisites: EC2100 and ability to program in MATLAB.
EC2400 Discrete Systems (3-1) Spring/Fall
Principles of discrete systems, including modeling, analysis and design. Topics include difference equations, convolution, stability, bilateral z-transforms and application to right-sided and left-sided sequences, system diagrams and realizations, and frequency response. Simple digital filters are designed and analyzed. Prerequisites: MA1113 and ability to program in MATLAB.
EC2410 Analysis of Signals and Systems (3-1) Summer/Winter
Analysis of digital and analog signals in the frequency domain; properties and applications of the discrete Fourier transform, the Fourier series, and the continuous Fourier transform; analysis of continuous systems using convolution and frequency domain methods; applications to sampling, windowing, and amplitude modulation and demodulation systems. Prerequisites: EC2400.
EC2450 Accelerated Review of Signals and Systems (4-0) As Required
An advanced review of continuous and discrete system theory intended for students who have previous education in these areas. Topics covered by each student will depend upon background and competence in the subject matter of EC2400, EC2410, and EC2320. Prerequisites: Sufficient background in linear systems theory. Graded on Pass/Fail basis only.
EC2500 Communications Systems (3-2) Spring/Fall
In this first course on the electrical transmission of signals, the theory, design, and operation of analog and digital communication systems are investigated. Included are A/D conversion, modulation, demodulation, frequency-division multiplexing, and time-division multiplexing. Prerequisites: EC2200 and EC2410.
EC2650 Fundamentals of Electromagnetic Fields (4-1) Spring/Fall
This course covers electromagnetic field theory and engineering applications. Both static and dynamic electric and magnetic field theory is covered. The complete theory is presented in terms of Maxwell's equations and boundary conditions. Applications include induction, plane wave propagation in lossless and lossy media, analysis of finite transmission lines, and plane wave reflection. Labs provide practical experience with microwave instruments, components, and measurement techniques. Prerequisites: MA1116 or equivalent.
EC2820 Digital Logic Circuits (3-2) Spring/Fall
An introductory course in the analysis and design of digital logic circuits that are the basis for military and civilian computers and digital systems. No previous background in digital concepts or electrical engineering is assumed. Topics include: data representation, Boolean algebra, logic function minimization, the design and application of combinatorial and sequential SSI, MSI, and LSI logic functions including PLAs and ROMs, and the fundamentals of finite state machine design and applications. Laboratories are devoted to the analysis, design, implementation, construction, and debugging of combinatorial and sequential logic circuits using SSI, MSI, LSI, and programmable logic devices. Prerequisites: None.
EC2840 Introduction to Microprocessors (3-2) Summer/Winter
An introduction to the organization and operation of micro processing and microcomputers, both key embedded elements of military systems. Topics include: the instruction set, addressing methods, data types and number systems, stack and register organization, exception processing, assembly language programming techniques including macros, assembly language implementation of typical control structures, data structures, and subroutine linkage methods. Laboratory sessions teach a systematic method for program design and implementation. The laboratory assignments consist of a series of programs which collectively implement a major software project. Prerequisites: A high level language.
EC2990 Design Projects in Electrical Engineering (0-8) Spring/Summer/Fall/Winter
Design projects under the supervision of faculty members. Individual or team projects involving the design of devices or systems. Projects will typically be in support of faculty members. Prerequisites: Consent of instructor. Graded on Pass/Fail basis only.
EC3000 Introduction to Graduate Research (1-0) Spring/Summer/Fall/Winter
This course is designed to prepare students to undertake graduate research and to write a thesis or dissertation. The first part of the course provides an overview of (1) the NPS Department of Electrical and Computer Engineering, the department's research program and its faculty, (2) the NPS Research Program and the organization and functions of the NPS Research Office, (3) NPS library electronic resources, (4) an overview of S&T planning in the DoD, and (5) guidance on the thesis process. In the second part of the course, research opportunities are presented by the faculty. A broader view of the field of electrical and computer engineering is gained through student attendance at ECE Department seminars delivered by outside speakers. In the third part of the course, students are exposed to thesis research currently being carried out in the ECE Department by attending thesis presentations delivered by graduating students. Prerequisites: Consent of instructor. Graded on Pass/Fail basis only.
EC3130 Electrical Machinery Theory (4-2) Winter
An introduction to the analysis of magnetically-coupled circuits, dc machines, induction machines, and synchronous machines. The course will include explicit derivations of torque, voltage, and flux linkage equations, formulation of steady-state circuits, development of reference frame theory, and the basics of machine simulation as required in shipboard electric drive analysis. Prerequisites: EC2110 (may be taken concurrently).
EC3150 Solid State Power Conversion (3-2) Summer
A detailed analytical approach is presented for the operation, performance, and control of the important types of solid state power converters found in naval shipboard power systems. The course reviews the characteristics of power semiconductor switching devices. A systems approach is used to analyze high power converters: phase controlled rectifiers, line commutated inverters, self-commutated inverters, transistor converters, and switching regulators. Prerequisites: EC2100 or consent of instructor.
EC3200 Advanced Electronics Engineering (3-2) Spring
Characteristics of differential and multistage amplifiers. Transistors frequency response, including Bipolar Junction Transistors (BJT), Junction Field Effect Transistors (JFET), and Metal Oxide Semiconductor Field Effect Transistors (MOSFET); characteristics and design consideration. Integrated circuit OPAMP applications; analysis and design of non-ideal OPAMPs. Applications of BJTs and Complementary Metal Oxide Semiconductors (CMOS) in integrated circuits, and different biasing techniques. Analysis and design of digital circuits, including Transistor Logic (TTL), Emitter Coupled Logic (ECL), and CMOS logic families. Applications and design feedback amplifiers and operational amplifiers applications in analog filters and oscillators. Prerequisites: EC2200.
EC3210 Introduction to Electro-Optical Engineering (4-1) Fall
An overview of the elements that comprise current military electro-optical and infrared (EO/IR) systems. Topics include properties of light, optical elements, quantum theory of light emission, operating principles of laser sources, propagation of Gaussian beams, laser sources, laser modulators, thermal sources of radiation, laser and IR detectors (photomultipliers, photoconductors, photodiodes, avalanche photodiodes), signal-to-noise analysis of direct- and heterodyne-receiver systems. Includes military applications of electro-optic and infrared technology such as missile seekers, laser designators, laser weapons, and Bragg-cell signal processors. Prerequisites: EC2200 and EC2650.
EC3220 Semiconductor Device Technologies (3-2) Fall
This course is intended to familiarize the student with solid state device operation and fabrication of present day semiconductors and transistor technologies. Topics include: fundamental theory of charge transport, semiconductor materials (Si, GaAs, SiGe, InP), bandgap engineering, epitaxy crystal growth, and semiconductor device manufacturing technology. A virtual wager lab is accomplished in the software labs to visualize parameters as impurity implants to electron flow. Measurement labs will utilize hands-on wafter probe measurements of digital and analog devices. Prerequisites: EC2200 or equivalent.
EC3230 Space Power and Radiation Effects (Formerly EO3205) (3-1) Spring
Fundamentals of different power systems utilized in spacecraft; photovoltaic power technology; solid-state physics, silicon solar cells, solar cell measurement and modeling, gallium arsenide cells and II-V compounds in general, array designs and solar dynamics. Radiation effects on solid state devices and materials. Survivability of solar cells and integrated circuits in space environment and annealing method. Other space power systems including chemical and nuclear (radioisotope thermoelectric generators and nuclear reactors). Energy storage devices and power conversion. Spacecraft power supply design. Note: EC3230 is taught with compressed scheduling (first six weeks of quarter). Prerequisites: EC2200.
EC3310 Optimal Estimation: Sensor and Data Association (3-2) Winter/Summer
The subject of this course is optimal estimation and Kalman filtering with extensions to sensor fusion and data association. Main topics include the theory of optimal and recursive estimation in linear (Kalman filter) and nonlinear (extended Kalman filter) systems, with applications to target tracking. Topics directly related to applications, such as basic properties of sensors, target tracking models, multihypothesis data association algorithms, reduced order probabilistic models and heuristic techniques, will also be discussed. Examples and projects will be drawn from radar, EW, and ASW systems. Prerequisites: EC2320, EC2010, MA3046.
EC3320 Optimal Control Systems (3-2) Spring
This course addresses the problem of designing control systems which meet given optimization criteria. The student is exposed to the development of the theory, from dynamic programming to the calculus of variation, and learns how to apply it in control engineering. Prerequisites: EC2300, EC2320.
EC3400 Digital Signal Processing (3-1) Spring/Fall
The foundations of one-dimensional digital signal processing techniques are developed. Topics include Fast Fourier Transform (FFT) algorithms, block convolution, the use of DFT and FFT to compute convolution, and design methods for nonrecursive and recursive digital filters. Multirate signal processing techniques are also introduced for sampling rate conversion, efficient analog to digital, digital to analog conversion, time frequency decomposition using filter banks and quadrature mirror filters. Computer-aided design techniques are emphasized. The algorithms introduced have direct applications in sonar and radar signal processing, IR sensor arrays, modern navy weapon systems, and also in voice and data communications. Prerequisites: EC2410.
EC3410 Discrete-Time Random Signals (3-2) Summer/Winter
Fundamentals of random processes are developed with an emphasis on discrete time for digital signal processing, control, and communications. Parameter estimation concepts are introduced, and impact of uncertainty in parameter evaluation (estimated moments and confidence intervals) are presented. Random processes are introduced. DKLT and applications to image processing and classification problems are considered. Impact of linear transformations to linear systems is discussed. FIR Wiener, and matched filters are introduced. IIR Wiener filter introduced, time permitting. Applications to signal and system characterization in areas such as system identification, forecasting, and equalizations are considered to illustrate concepts discussed during the course. Prerequisites: EC2410 (may be concurrent) and EC2010.
EC3450 Fundamentals of Ocean Acoustics (4-0) Fall
Introduction to various mathematical techniques (both exact and approximate), special functions (e.g., Bessel functions, Hankel functions, and Legendre polynomials), orthogonality relationships, etc., that are used to model and solve real world problems concerning the propagation of sound in the ocean. Topics include, for example, reflection and transmission coefficients, ocean waveguide pulse-propagation models based on normal mode and full-wave theory, the WKB approximation, three-dimensional ray acoustics, and the parabolic equation approximation. Prerequisites: Standard undergraduate sequence of calculus and physics courses for engineering and science students.
EC3500 Analysis of Random Signals (4-0) Spring/Fall
Fundamental concepts and useful tools for analyzing non-deterministic signals and noise in military communication, control, and signal processing systems are developed. Topics include properties of random processes, correlation functions, energy and spectral densities, linear systems and mean square estimation, noise models and special processes. Prerequisites: EC2500 (may be concurrent) and EC2010, or consent of instructor.
EC3510 Communications Engineering (Unclassified) 3-1 (Summer/Winter)
The influence of noise and interference on the design and selection of digital and analog communications systems is analyzed. Topics include link budget analysis and signal-to-noise ratio calculations, receiver performance for various analog and digital modulation techniques, and bandwidth and signal power trade-offs. Examples of military communications systems are included. Prerequisites: EC2220 and EC3500 or EC3410.
EC3550 Fiber Optic Systems (3-1) Fall
An introduction to the components and to the concepts of designing fiber optic communications systems for military applications. Includes fiber properties and parameters, fiber fabrication and testing, LED and injection laser sources, pin photodiodes and avalanche photodiode detectors, receiver design considerations, connector and splice techniques, and system design incorporating analysis and trade-offs. Data distribution techniques are also studied. Prerequisites: