ECSE-443 Introduction 2010 Handout

ECSE-443 Introduction 2010 Handout - 1 Introduction to...

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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 procédures disciplinaires. 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 ...
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This note was uploaded on 09/16/2011 for the course ECSE 361 taught by Professor Franciscodgaliana during the Winter '09 term at McGill.

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