This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 1 Introduction to Numerical Methods
in Electrical Engineering Text: Second Edition, McGraw-Hill, 2008. ECSE 443 Note: A “working knowledge” of MATLAB will be
required to do the course assignments! January 2010 General Information
Lectures: MWF 10:35 – 11:25 Tutorials: Wed 17:35 – 19:25 TR-0070 Fri 13:35 – 15:25 TR-2120 ? Tutors: Adrian Ngoly & Maryam Golshayan Advising: T.B.A. Professor: Steve McFee Advising: MWF 11:35 – 12:25 Applied Numerical Methods with MATLAB
for Engineers and Scientists, S.C. Chapra, Rm. T.B.A. Prerequisites: ECSE 221, ECSE 330, ECSE 351 or
ECSE 353 (only for CE students). Help? Two introductory lectures will be given on
MATLAB, and the text should be helpful
for student review / remedial self-study. Course Objective
The purpose of ECSE 443 is to introduce the key
theoretical concepts and practical applications of
the fundamental numerical methods used in EE.
The teaching approach is focused on the methods,
and how to use them; not on derivations or proofs.
The objective is to develop “practical knowledge”. 2 3 Tentative Course Evaluation
Class Test #1 20 marks (March 1) Class Test #2 20 marks (March 29) Assignment #1 15 marks (1/29 – 2/12) Assignment #2 15 marks (2/12 - 3/5) Assignment #3 15 marks (3/5 – 3/19) Assignment #4 15 marks (3/19 – 4/9) Note
The “tentative” aspects of this evaluation scheme
only pertain to the dates and individual values for
the assignments (the total allotment of 60 marks
for assignments is fixed); the test dates are firm.
L There will not be a Final Exam for this course. In accord with McGill University’s Charter of
Students’ Rights, students in this course have the
right to submit in English or in French any written
work that is to be graded. Lecture Material and Handouts
The intention is to present much (hopefully half?)
of the lecture material for ECSE 443 using slides.
The students will be given copies of this material.
However, a significant amount of the lectures will
be presented using the blackboard. The students
will need to be prepared to take notes in lectures!
Further, the lectures are not designed to replace
the text; the students will need to read the text! Tutorials
Scheduled tutorials will be held weekly to provide
teaching support for the required course content.
Tutorials will not be used to teach any new course
material, however some tutorial slots may be used
for MATLAB review, and for Class Test solutions.
Tutor: Adrian Ngoly ([email protected]) 4 Assignments
Assignments form an important part of ECSE 443
and they will count highly in the course evaluation!
The assignments will target all key aspects of the
course, and they are intended to promote student
self-learning, and to serve for student evaluation.
Each assignment will require the student to carry
out original MATLAB programming and computing;
MATLAB M-files must be submitted for testing!
Although the assignments are MATLAB oriented,
associated theoretical questions or non-MATLAB
calculations (e.g. analytical) also may be required. Important!
It is strongly recommended that students try to
understand and do their assignments individually.
Marker: 5 Maryam Golshayan
([email protected]) Academic Integrity at McGill University
McGill University values academic integrity. Therefore all
students must understand the meaning and consequences
of cheating, plagiarism and other academic offences under
the Code of Student Conduct and Disciplinary Procedures.
L see www.mcgill.ca/integrity for more information. (Official Translation – Office of the Provost)
L'université McGill attache une haute importance à
l'honnêteté académique. Il incombe par conséquent à
tous les étudiants de comprendre ce que l'on entend par
tricherie, plagiat et autres infractions académiques,
ainsi que les conséquences que peuvent avoir de telles
actions, selon le Code de conduite de l'étudiant et des
L pour de plus amples reseignements, veuillez
consulter le site www.mcgill.ca/integrity. 6 Course Contents
1. 7 Modeling, Computers and Error Analysis.
(a) Concept of numerical methods.
(b) Context of numerical methods.
(c) Issues with numerical methods.
(d) Classes of numerical methods.
(e) Common modeling terminology.
(f) Accuracy and precision issues.
(g) Absolute and relative errors.
(h) Round-off errors.
(i) Truncation errors.
(j) Total numerical error. Note: The content listed above is addressed by
Chapters 1 and 4 of the text; Chapters 2
and 3 contain MATLAB review materials.
(It is highly recommended to review these
two MATLAB chapters - starting tonight!) 2. Equation Roots and Optimization.
(a) Graphical approaches for roots.
(b) Bracketing concepts and roots.
(c) Bisection method for roots.
(d) False position method for roots.
(e) Fixed-point iteration for roots.
(f) Newton-Raphson method for roots.
(g) Secant methods for roots.
(h) Polynomials and roots (time permitting).
(i) One-dimensional optimization.
(j) Golden-section search and optimization.
(k) Parabolic interpolation and optimization.
(l) Multidimensional optimization (hopefully).
Note: Addressed by Chapters 5, 6 and 7 in text.
Solving for roots of equations and solving
optimization problems are closely related
mathematical concepts, and the numerical
methods applicable to both are analogous. 8 9 3. Linear Systems and Nonlinear Considerations. 4. Curve Fitting. (a) Matrix algebra concepts. (a) Statistical analysis concepts. (b) Naïve Gauss elimination. (b) Linear least squares regression. (c) Matrix element pivoting. (c) Linearization of nonlinear relationships. (d) LU matrix factorization. (d) Polynomial regression methods. (e) Cholesky factorization. (e) Multiple linear regression methods. (f) Matrix inverse. (f) Generalized linear least squares. (g) Error analysis and system condition. (g) Nonlinear regression methods. (h) Gauss-Seidel method and Jacobi iteration. (h) Interpolation concepts. (i) Properties of nonlinear systems (N.L.S.) (i) Newton interpolation polynomials. (j) Successive substitution method for N.L.S. (j) Lagrange interpolation polynomials. (k) Newton-Raphson method for N.L.S. (k) Inverse interpolation concepts.
(l) Extrapolation concepts. Note: Content is covered by text Chapters 8-12.
Although this section primarily focuses on
numerical methods for linear systems, the
basic issues and fundamental methods for
nonlinear systems are also introduced and
examined to give context and perspective. (m) Principles of splines (time permitting).
(n) Piecewise polynomial interpolation.
Note: Material covered by text Chapters 13-16.
Text detail exceeds course requirements! 10 11 5. Integration and Differentiation. 6. Ordinary Differential Equations. (a) Fundamentals of numerical integration. (a) Fundamentals of “numerical” ODEs. (b) Newton-Cotes integration formulas. (b) Basic Euler’s methods for ODEs. (c) Trapezoidal rule for integration. (c) Improved Euler’s methods. (d) Simpson’s rules for integration. (d) Runge-Kutta methods for ODEs. (e) Higher-order Newton-Cotes formulas. (e) Approaches for systems of ODEs. (f) Multiple integral concepts. (f) Adaptive Runge-Kutta methods. (g) Integrating functions vs. values. (g) Multistep methods for ODEs. (h) Romberg integration methods. (h) Implications of ODE stiffness. (i) Gauss quadrature methods. (i) Fundamentals of “numerical” BVPs. (j) Adaptive quadrature approaches. (j) The shooting method for BVPs. (k) Numerical differentiation fundamentals. (k) Finite difference methods. (l) High-accuracy differentiation formulas. (l) Finite element methods (time permitting). (m) Richardson extrapolation applications.
(n) Derivatives of unequally spaced data.
(o) Partial derivative approaches.
Note: Material covered by text Chapters 17-19. Note: Material covered by text Chapters 20-22.
Course content may extend beyond detail
provided in text for some of these topics. 12 ...
View Full Document
This note was uploaded on 09/16/2011 for the course ECSE 361 taught by Professor Franciscodgaliana during the Winter '09 term at McGill.
- Winter '09