AMS 211 - Fall 2007

Foundations of Applied Mathematics

This class is a one-quarter accelerated course on basic mathematical methods typically used in Applied Mathematics and many physical and engineering sciences.

The intended audience is graduate students from numerous departments in all physical and engineering Sciences (e.g. Earth & Planetary Sciences, Applied Mathematics & Statistics, Astronomy & Astrophysics, Ocean Sciences, Physics, Chemistry, Electrical Engineering, etc) who need to solidify their fundamental knowledge of the tools used in Applied Mathematics.

Required textbook is:

K.F. Riley, M.P. Hobson, & S.J. Bence, "Mathematical methods for Physics and Engineering", 3rd edition, Cambridge University Press.

Recommended further reading can be found in:

Arfken, G., "Mathematical Methods for Physicists", Academic Press
Strang, G., "Introduction to Applied Mathematics", Wellesley Cambridge Press
Courant, R. & Hilbert, D., "Methods of Mathematical Physics", Wiley Interscience.

All students will be evaluated based on regular homework assignments involving the mathematical solution of topical problems. The students will be required to pass a final examination.

Week-by-week (roughly) topics are selected chapters from the main textbook:

Week 1-4: Multivariate Calculus and Linear Algebra
- Chapter 5: Partial Differentiation
- Chapter 6: Multiple integrals
- Chapter 8: Matrices and Vector spaces
- Chapter 10: Vector Calculus
- Chapter 11: Line, Surface and Volume Integrals
Week 5: Fourier Series & Transforms
- Chapter 12: Fourier Series
- Chapter 13: Integral Transforms
Week 6: Complex variables and applications
- Chapter 24: Complex variables
- Chapter 25: Applications of complex variables.
Week 7-10: ODEs
- Chapter 14: First order ODEs
- Chapter 15: Higher order ODEs
- Chapter 17: Eigenfunction methods for Differential Equations
- Chapter 18: Special Functions

General Class Information

Class Newsgroup:

NEWSGROUP - for announcements, general discussion, and help

Lecture times:

Tues Thurs, 12:00-01:45pm, Phys Sci 136

Instructor:

Name: Nic Brummell (brummell@soe.ucsc.edu)

Phone: 9-2122

Office: BE 125

Instructor Office Hours:

Tues Thurs 4-5pm