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CHE 5480
ADVANCED MATHEMATICAL
METHODS IN ENGINEERING
FALL 2001
School of Chemical Engineering & Materials Science
Instructor: Professor Miguel J. Bagajewicz
Email:Prof. Miguel 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 anappointment, 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)
mailto:%[email protected]:%[email protected]:%[email protected]://www.ou.edu/class/che-designhttp://www.ou.edu/class/che-designhttp://www.ou.edu/class/che-designhttp://www.ou.edu/class/che-design/Advanced-Math/indexhttp://www.ou.edu/class/che-design/Advanced-Math/indexhttp://www.ou.edu/class/che-design/Advanced-Math/indexhttp://www.ou.edu/class/che-design/Advanced-Math/Lectures-Hwk.htmhttp://www.ou.edu/class/che-design/Advanced-Math/Lectures-Hwk.htmhttp://www.ou.edu/class/che-design/Advanced-Math/Lectures-Hwk.htmhttp://www.ou.edu/class/che-design/Advanced-Math/indexhttp://www.ou.edu/class/che-designmailto:%[email protected]
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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. HamiltonCayley 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
ofsingular 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:
1. Late homework or reports loose their value exponentially. The
time constant is0.25/day.
2.No makeup exams.
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3. Class attendance is required.4. 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 herabilities
should contact the instructorpersonally as soon as
possible so accommodations necessary to ensure full
participation and facilitate his/her
educationalopportunities are discussed
