ECE 495Z - Numerical Methods for Electrical and Computer Engineers

Lecture Hours: 3 Credits: 3

Counts as:

Experimental Course Offered: Fall 2006

Catalog Description:
An introduction to numerical methods for Electrical and Computer Engineers; the objective of this course is to introduce the basic numerical toolset needed for ECE students to solve problems arising in different areas of ECE, including signal processing, linear system theory, and semiconductor physics. The course will include the following topics: Floating-point representation; sources and propagation of errors and stability in numerical analysis; Numerical methods for systems of linear and non-linear equations; Numerical integration and approximation theory along with basic methods for differential equations; Introduction into numerical optimization; minimization for constrained and unconstrained optimization; Iterative methods for sparse systems of linear equations. These concepts and techniques are illustrated through the introduction of both classical and modern ECE based applications.

Required Text(s): None.

Recommended Text(s):
  1. Introduction to Numerical Analysis, Current Edition, Kendall E. Atkinson, Wiley, 1989, ISBN No. 0471624896.
  2. Matrix Computations, Current Edition, Golub and Van Loan, Johns Hopkins University Press, 1996, ISBN No. 0801854148.
  3. Numerical Linear Algebra, Current Edition, Trefethen and Bau, Soc for Industrial & Applied Math, 1997, ISBN No. 0898713617.

Learning Outcomes:

A student who successfully fulfills the course requirements will have demonstrated:
  1. understanding of the necessity of numerical solutions to mathematical problems arising in engineering. [a,h,j,k]
  2. understanding of, and an ability to apply basic algorithms of numerical linear algebra for ECE applications. [a,b,c,e,g,h,j,k]
  3. basic understanding of the formulation of commonly encountered ECE problems into either constrained or unconstrained optimization problems. [a,b,c,e,g,h,j,k]
  4. an ability to use mathematical software for the solution of optimization problems arising in ECE. [a,b,c,e,f,j,k]

Lecture Outline:

Week(s) Topic(s)
1 Computer Representation: Floating-point representations, sources and propagation of error, stability.
2,3 Non-linear equations: Newtons Method, Secant Method, convergence and accuracy of general one-point iteration methods.
4 Approximation methods and numerical integration: Trapezoidal rule, Simpsonsrule..
5,6 Methods for differential equations: Euler and Runge-Kutta Methods, initial value problems, boundary value problems.
7 Systems of linear equations: LU factorization, Gaussian Elimination, pivoting and stability.
8,9 Orthogonality: Projections, QR Factorization, and the Gram-Schmidt process.
10,11 Unconstrained optimization: Minimizers, Gradient Methods, and Conjugate Direction Algorithm.
12,13 Constrained optimization: Lagrangian methods, equality and inequality constraints.
14,15 Iterative methods: Arnoldi Iteration, GMRES, Lanczos Iteration, Conjugate Gradient, and Preconditioning.

Engineering Design Content:

Establishment of Objectives and Criteria
Synthesis
Construction
Evaluation

Engineering Design Consideration(s):

Economic
Sustainability