AMATH 401

INTRODUCTION TO METHODS IN APPLIED MATHEMATICS I

FALL 2003

INSTRUCTOR:

Name:		Mark Kot
Office:		408B Guggenheim
Phone:		543-0908
Fax:		685-1440
Email:		kot@amath.washington.edu
Office Hours:	M, W, F  2:30-3:20 pm

TEACHING ASSISTANTS:

Name:		Damon Toth
Office:		436 Johnson
Phone:		616-8703
Fax:		685-1440
Email:		dtoth@amath.washington.edu
Office Hours:	Thursday  1:30-3:30 pm

Name:		Santosh Srivastava
Office:		405D Guggenheim
Phone:		543-0319
Fax:		685-1440
Email:		santosh@amath.washington.edu
Office Hours:	Tuesday  10:30-11:20 am

MEETING TIMES:

M, T, W, F	1:30-2:20 pm	Guggenheim 217

LECTURE NOTES:

topic_01.pdf     Introduction
topic_02.pdf     Vector algebra
topic_03.pdf     Vector functions
topic_04.pdf     Scalar and vector fields
topic_05.pdf     Special coordinate systems
topic_06.pdf     Rate of change of vector fields
topic_07.pdf     Line integrals
topic_08.pdf     Surface integrals
topic_09.pdf     Stokes' theorem
topic_10.pdf     Volume integrals
topic_11.pdf     Complex algebra
topic_12.pdf     Analyticity
topic_13.pdf     Elementary functions
topic_14.pdf     Integration
topic_15.pdf     Power series
topic_16.pdf     Calculus of residues
topic_17.pdf     More residues
topic_18.pdf     Even more residues

VIDEOS:

You may download lectures from the class
EDGE streaming video site.

To read more about streaming video see the
EDGE information page.

You can also view videos at Odegaard library.

COURSE TEXT:

Saff, E. B. and Snider, A. D.  2003.
Fundamentals of Complex Analysis with Applications to Engineering and Science
Prentice-Hall, Upper Saddle River, New Jersey.

ISBN 0-13-907874-6 (Hardcover)

The text is optional.
Older editions of the text are quite usable and may be more affordable.

COURSE CONTENT:

Vector Analysis (3-4 weeks)

Vector fields and vector calculus Orthogonal curvilinear coordinates Gradient, divergence, and curl Line, surface, and volume integrals

Green's theorem, Stokes' theorem, and divergence theorem.

Complex Analysis (6-7 weeks)

Complex numbers Functions of a complex variable Analyticity Integration Cauchy's theorem and the Cauchy integral formula Taylor and Laurent series Calculus of residues and contour integration

Fourier and Laplace transforms.

PREREQUISITES:

You should already know some vector algebra and some multivariate calculus.
It helps if you are familiar with infinite sequences and series.

HOMEWORK:

I will assign weekly problem sets.
Homeworks constitute 40% of the final grade!
Write up your homework alone, not as a group!

hw1.pdf     Due:  10/10/2003
hw2.pdf     Due:  10/17/2003
hw3.pdf     Due:  10/24/2003
hw4.pdf     Due:  11/10/2003
hw5.pdf     Due:  11/17/2003
hw6.pdf     Due:  11/26/2003
hw7.pdf     Due:  12/03/2003
hw8.pdf     Due:  12/10/2003

EXAM PRACTICE PROBLEMS:

practice1.pdf
practice2.pdf

EXAMS:

There will be a midterm and a final.
Exams constitute 60% of the final grade.  
The final counts more than the midterm.

IMPORTANT DATES:

    +----------+--------------+-----------------------------+
    | Monday   | September 29 |        Classes Begin        |
    +----------+--------------+-----------------------------+
    | Monday   |  October 27  |           Midterm           |
    +----------+--------------+-----------------------------+
    | Tuesday  | November 11  | Veterans Day     No Class   |
    +----------+--------------+-----------------------------+
    |Thursday  | November 27  | Thanksgiving     No Class   |
    | Friday   | November 28  |                  No Class   |
    +----------+--------------+-----------------------------+
    |Wednesday | December 10  |        Last Lecture         |
    +----------+--------------+-----------------------------+
    | Friday   | December 12  |  Final Exam    2:30-4:20 pm |
    +----------+--------------+-----------------------------+

You can view the official academic calendar at
2003 Academic Calendar.

You can examine the official exam schedule at
Autumn 2003 Final Exam Schedule.

OTHER USEFUL BOOKS AND REFERENCES:

Vector Analysis

Davis, H. F. and Snider, A. D. 1995. Introduction to Vector Analysis. Wm. C. Brown Publishers, Dubuque, IA. Rahman, M. 2001. Applied Vector Analysis. CRC Press, Boca Raton, FL. Schey, H. M. 1992. Div, Grad, Curl, and All That: An Informal Text on Vector Analysis. Norton, New York, NY.

Schwartz, M., Green, S. and Rutledge, W. A. 1960. Vector Analysis with Applications to Geometry and Physics, Harper & Brothers, New York, NY.

Complex Analysis

Ablowitz, M. J. and Fokas, A. S. 1997. Complex Variables: Introduction and Applications. Cambridge University Press, Cambridge, UK. Brown, J. W. and Churchill, R. V. 1996. Complex Variables & Applications. McGraw-Hill, New York, NY. Kwok, Y. K. 2003. Applied Complex Variables for Scientists and Engineers. Cambridge University Press, Cambridge, UK. Marsden, J. E. and Hoffman, M. J. 1999. Basic Complex Analysis. W. H. Freeman, New York, NY. Mathews, J. H. and Howell, R. W. 2001. Complex Analysis for Mathematics and Engineering. Jones and Bartlett, Sudbury, MA. Polya, G. and Latta, G. 1974. Complex Variables. John Wiley & Sons, New York, NY. Rubenfeld, L. A. 1985. A First Course in Applied Complex Variables. John Wiley & Sons, New York, NY.

Spiegel, M. R. 1968. Schaum's Outline of Complex Variables. McGraw-Hill, New York, NY.