CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA
EGR 599
ADVANCED ENGINEERING MATHEMATICS
Spring 2005
Instructor: Thuan K. Nguyen, email: TKNguyen@csupomona.edu
Office Hour: MW 10:30-11:30 A.M, 5:30-6:00 PM, TTh. 8-9:00 AM.
Room:
13-226
Phone: 869-2631
http://www.csupomona.edu/~tknguyen/
TEXT(Optional): Mathematical Methods for Scientists and Engineers by Donald A.
McQuarrie
REFERENCES:
(1) Partial Differential Equations and Boundary Value Problems by Nakhle Asmar.
(2) Advanced Engineering Mathematics by 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
1
TOPICS
Basic Properties of Matrices. Matlab Matrix Operations.
CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA
Square and Symmetric Matrices. Determinants and Matrix Inverses.
Orthogonal and Triangular Matrices. Systems of Linear Equations
2
Matlab Matrix Functions. Linear Transformations.
Eigenvalues and Eigenvectors. Complex Vectors and Matrices
3
Matlab Commands for Eigenvectors. Matrix Calculus.
Applications to Differential Equations. Quiz #1, Oct. 15 2003
4
Classification of Differential Equations. Linear Differential Equations.
Higher Order Differential Equations.
5
Particular Solutions of Differential Equations. Systems of Differential Equations.
Matlab Solutions of Systems of Differential Equations. Quiz #2, Oct. 29 2003
6
Homogeneous Systems with Repeated Eigenvalues.
Nonhomogeneous Systems of Differential Equations.
Transforming Differential Equations.
7
Periodic Functions. Trigonometric Series. Fourier Series.
Even and Odd Functions. Half-Range Expansions. Quiz #3, Nov. 12 2003
8
The Fourier Transform and its Applications
Discrete and Fast Fourier Transforms. Matlab Fourier Commands.
9
Introduction to Partial Differential Equations.
Separation of Variables. Use of Fourier Series.
D'Alembert's Solution of the Wave Equation. Quiz #4, Nov. 26 2003
10
Heat 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
CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA
answers that do not show the work involved. Staple all pages of an assignment together in the
upper left corner.