University of California, Davis
Department of Chemical Engineering and
Materials Science
ECH 259: Applied Mathematics
(CRN# 38994)
Fall Quarter 2004
MWR (11:00-11:50 AM) Room: Bainer 1134
R (3:10-4:00 PM) Room: Pysics/Geo 140
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| Instructors: |
Brian G. Higgins |
| Office : |
Bainer 3012 |
| Office Hours: |
T&F 1-2:00 pm |
| Phone: |
752-8780 |
| e-mail: |
bghiggins@ucdavis.edu |
Course Overview
ECH259: Advanced Engineering Mathematics will be devoted to the study of nonlinear partial
differential equations (PDE) with relevance to chemical engineering; examples will be drawn
from various branches of engineering science. The first part of the course will cover
several methods that are useful for finding analytical solutions for linear systems:
separation of variables, Laplace/Fourier Transforms. This will be the basis for developing
concepts and techniques for describing nonlinear systems. The course will make extensive use
of the software package "Mathematica". Finite difference techniques and continuation methods
will be used to study the solution space for nonlinear PDEs. The prerequisites for Advanced
Engineering Mathematics are: Mathematics 22B, 21C, 22A, 22D. If you do not meet the prerequisites,
or are unsure if you do, please contact me bghiggins@ucdavis.edu.
The text for the course is Elementary Applied Partial differential Equations (fourth edition),
by Richard Haberman. It is available in the UCD Bookstore. You may also order it through an
online bookstore such as Amazon Books. From time to time I will be posting selected lecture notes and
reading material on the Web. Please use the following link to access these notes: ECH 259 Class
Notes.
In addition to the ECH 259 lectures, I will be offering a 2 unit course ECH 198: Introduction
to Mathematica, for students interested in learning more about how to use Mathematica to solve
engineering problems. The class for this course will meet on Tuesday 10:00-12:00 Noon in
Academic Surge 1116. The CRN# is 68725 and it will graded as P/NP. Attendance in ECH 198 is
optional, but is strongly encouraged.
The following Concepts & Skills will be emphasized in ECH 259
CONCEPTS
- Homogeneous versus inhomogeneous differential equations
- Homogeneous solutions and particular solutions of ODEs
- Derivation of PDEs from conservation principles.
- General solution of linear PDEs (heat equation, Laplace equation)
- Fourier series and Sturm Lioville theory
- Orthogonal functions,eigenvalues & eigenvectors
- Dynamical systems, concept of bifurcation, linear stability
- Stable and unstable manifolds; Hartman-Grobman theorem; portrait of equilibrium points
- Reaction diffusion equations, spatial patterns, multiple solutions, and bifurcation
SKILLS
- Solution of first order and second order ODEs.
- Separation of variables 1-D and 2-D transient heat conduction equation (various coordinate systems).
- Separation of Variables Laplace equation (various coordinate systems).
- Analysis of dynamical systems
- Analysis of reaction diffusion systems
The text for the course is : Elementary Applied Partial differential Equations (fourth edition), by Richard Haberman
Course Grade
The overall letter grade for the course will be determined as follows:
One midterm 30% , final exam 50%, and Homework 20%.
The final examination will take place on
Saturday, December 18, from 1:30-3:30PM in
Bainer 1134.
Plan now to take this examination at the scheduled time.
Please note that this time and place has been designated by the Registrar. For further details on
exam policy, please link to Registar: Final Exams.
The time for the Mid-Term is:
Mid-Term #1: Monday November 15 (11:00-11:50 AM)
- Rules: If an emergency occurs and you need special attention, contact Professor Higgins as soon as possible.
All exams will be closed book and 1 sheet of notes.
No make-up exams will be given, and students who miss an exam for justifiable reasons will be assigned an
appropriate grade on the basis of their scores in the other exams.
- Integrity: Perhaps the most productive learning atmosphere occurs when you ask a question,
thus you are encouraged to ask questions in class and while studying with other students.
Questions and answers help to clarify concepts, and you are encouraged to share concepts and
ideas concerning homework problems. However, the work that you submit for a grade in this
course must be your own, i.e., you must be the master of the material to which you have
affixed your signature. Evidence of any violations of the UCD Code of Academic Conduct
will be sent directly to Student Judicial Affairs. If you are unsure of what is meant
by plagiarism, cheating, academic dishonesty, etc., see the UCD Code of Academic Conduct.
A brief explanation is given in the Schedule & Directory under the title of Integrity
and details are available here
Special Needs
If you have a disability that impacts on your learning, I encourage you to talk with me about it on a confidential basis so that we might collectively devise a strategy to overcome whatever barriers might exist.
Class Assistants
No TA has been assigned for this course.