CHE 5480

ADVANCED MATHEMATICAL METHODS IN ENGINEERING

FALL 2001

School of Chemical Engineering & Materials Science Instructor: Professor Miguel J. Bagajewicz

Research Group URL: http://www.ou.edu/class/che-design

Class URL: http://www.ou.edu/class/che-design/Advanced-Math

Lectures and Homework

Grader: To be announced.

Office Hours: I have an open door policy. Walk in my office every time you want and I will interrupt whatever I am doing. In case you feel better having an appointment, arrange for one. Two important rules to talk to me:

1. Make sure you thought about the problem and have some analysis to offer together with your question
2. Make sure you can explain you problem or make the question in one-two sentences.

SYLLABUS

The topics covered and the approximate time devoted to them is in the list below. The order of presentation and coverage will likely be altered.
Every effort will be made to make the material relate to the different disciplines spanned by the students attending the class.

Review Scalar and Vector Field Theory: Properties of div, curl, etc. Conservative fields. Tensor Algebra. (~1 week)
ODE: Linear equations with variable coefficients (Bessel equation, etc). Sturm Liouville Theory. Green Functions. Similarity transformations. Introduction to perturbation theory (inner and outer solutions + matching). (~ 5 weeks)
PDE: Separation of variables. Parabolic Elliptic and Hyperbolic Equations. Fourier series solutions. (~ 4 weeks)
Matrix Algebra: Definitions of Adjoint, Minors, Jacobians, Hessian. Eigenvalues. Eigenvectors. Hamilton Cayley Theorem. QR Decomposition. Quadratic Forms. Ill Conditioned Matrices (~3 weeks)
Complex Analysis: Function in the complex Domain (logarithm, etc). Poles and zeros. Line integrals. Fourier Transform. Integrals of singular integrals, and if there is time, conformal mapping. (~3 weeks)

Textbook:: Greenberg M., Advanced Engineering Mathematics. Prentice Hall. (1998)

Material will also be taken form

Loney N. Applied Mathematical Methods for Chemical Engineers. CRC Press, (2000).
Stackgold I. Green's Functions and Boundary Value Problems. Wiley (1998).
Wylie and Barrett. Advanced Engineering Mathematics. McGraw Hill. (1995).
Simmonds and Mann. A first Look at Perturbation Theory., Dover (1998)
Instructor Notes

Homework:

Homework will be assigned as frequently as once a week.

Grading System:

Homework 15%
Tests 55%
Final Exam 30%

A small project (read a paper, implement a certain procedure, etc) may be assigned. Grades from such projects will be considered as half a test.

Some Rules:

Late homework or reports loose their value exponentially. The time constant is 0.25/day.
No makeup exams.
Class attendance is required.
Other rules may be added.

Any student in this course who has a disability that may prevent him or her from fully demonstrating his or her abilities should contact the instructor personally as soon as possible so accommodations necessary to ensure full participation and facilitate his/her educational opportunities are discussed

Disclaimer