CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA
EGR 599 ADVANCED ENGINEERING MATHEMATICS Spring 2005
Instructor: Thuan K. Nguyen, email:
Office Hour: MW 10:30-11:30 A.M, 5:30-6:00 PM, TTh. 8-9:00 AM.
Room: 13-226Phone: 869-2631
TEXT(Optional): Mathematical Methods for Scientists and Engineersby Donald A. McQuarrie
REFERENCES:
(1) Partial Differential Equations and Boundary Value Problems by Nakhle Asmar.
(2) Advanced Engineering Mathematicsby Erwin Kreyszig
(3) Advanced Engineering Mathematics with MATLAB, 2e by Thomas Harman
GRADE:
At least 12 hours per week must be reserved to study and to do assignments for this class
No late homework. No make-up quizzes or tests
Homework (best 8 of 9 assignments) 15%
Best 3 of 4 quizzes (open text book only) 45%
Comprehensive Final (open text book only) 40%
93-100% A , 90-93% A- , 87-90% B+ , 83-87% B , 80-83% B- , 77-80% C+
70-77% C , 0-70% F
Catalog Description
EGR599 Advanced Engineering Mathematics (4)
The course presents mathematical techniques for practical applications in engineering. It basically will cover both differential equations and linear algebra, and introduce the MATLAB tools. The approach is to integrate analytical and computer solutions of problems that lead to understanding of advanced mathematical techniques. The course will provide many examples showing applications of mathematical principles using numerical and symbolic computer solutions. 4 lectures/problem-solving.
Prerequisite: Undergraduate course in differential equations.
Course Objectives
After completing this course the student will be able to …
1.Apply the matrix methods to solve practical problems in engineering.
2.Solve the system of first-order ODE (Ordinary Differential Equations).
3.Solve the linear ODE of second and higher order.
4.Apply the methods of Separation of Variable and Fourier Transform to solve the important linear partial differential equations of the second order (Laplace, Poisson, wave, and heat equations).
Topics Covered
WEEK TOPICS
1Basic Properties of Matrices. Matlab Matrix Operations.
Square and Symmetric Matrices. Determinants and Matrix Inverses.
Orthogonal and Triangular Matrices. Systems of Linear Equations
2Matlab Matrix Functions. Linear Transformations.
Eigenvalues and Eigenvectors. Complex Vectors and Matrices
3Matlab Commands for Eigenvectors. Matrix Calculus.
Applications to Differential Equations. Quiz #1, Oct. 15 2003
4Classification of Differential Equations. Linear Differential Equations.
Higher Order Differential Equations.
5Particular Solutions of Differential Equations. Systems of Differential Equations.
Matlab Solutions of Systems of Differential Equations. Quiz #2, Oct. 29 2003
6Homogeneous Systems with Repeated Eigenvalues.
Nonhomogeneous Systems of Differential Equations.
Transforming Differential Equations.
7Periodic Functions. Trigonometric Series. Fourier Series.
Even and Odd Functions. Half-Range Expansions. Quiz #3, Nov. 12 2003
8The Fourier Transform and its Applications
Discrete and Fast Fourier Transforms. Matlab Fourier Commands.
9Introduction to Partial Differential Equations.
Separation of Variables. Use of Fourier Series.
D'Alembert's Solution of the Wave Equation. Quiz #4, Nov. 26 2003
10Heat Equation: Solution by Fourier Series
Heat Equation: Solution by Fourier Integral.
Equations Solvable by the Matlab PDE Toolbox.
FINAL EXAM Monday, June 6, 6:00-8:00 PM
Homework
Homework must be turned in prior to the start of class on the day that it is due. No late homework will be accepted. Not all of the assigned problems will be graded, but you will not know in advance which will be graded, so it is best to do them all. An engineer's work should be neat, well organized, and easy to follow. Points may be deducted for work that does not adhere to this format. The following information must be on the top of the first page of your homework.
______
EGR599 Problem set #1 LAST NAME, FIRST 1/1
How you get your answer is very important in engineering, therefore show all of your work on assignments, quizzes, and exams. Mark your final answer clearly by drawing a box around it. Except for the questions that require you to fill in the blank, no credit will be given for final answers that do not show the work involved. Staple all pages of an assignment together in the upper left corner.