AMATH 501

Vector Calculus and Complex Variables
Fall 2013

Schedule

SLN:		10191 (Section A)
		10192 (Section B)
Days:		M, T, W, F
Time:		1:30-2:20 pm
Room:		Loew 216

• Current Section A Status

• Current Section B Status

Section A is the regular, on-campus, in-class section for graduate students.

Section B is for students in the EDGE program. For more about EDGE, please see the

• EDGE Program

Amath 501 is for graduate students. Undergraduates should sign up for Amath 401.

Instructor

Name:		Mark Kot
Office:		230B Lewis Hall
Phone:		(206) 543-0908
Fax:		(206) 685-1440
Email:		mark_kot@comcast.net

Office Hours:		M, W, F
		3:00-4:00 pm
		230B Lewis Hall

• Personal Web Page

Assistant

Name:		Pedro Maia
Office:		316 Lewis Hall
		(but please see office hours for meeting place)
Phone:		(206) 543-5493
Fax:		(206) 685-1440
Email:		theamathta@gmail.com

Office Hours:		M, T, W
		Tuesday is for Google Chat
		4:00-5:00 pm
		128 Lewis Hall

• Web Page

Content

Course Catalog

Vector analysis (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 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.

Textbooks

There are no required textbooks.

There are a limited number of appropriate vector-analysis ebooks available.
However the non-profit Internet Archive has a early edition of Davis and Snider's
popular book available online. Please see:

Davis, H. F. and Snider, A. D. 1979. Introduction to Vector Analysis. Allyn and Bacon, Boston.
Link to Textbook

The mathematics library has a number of Springer ebooks that can be
downloaded and used as textbooks for the complex-variables portion of
the course. For examples, please see:

Agarwal, R. P., Perera, K., and Pinelas, S. 2011. An Introduction to Complex Analysis. Springer, New York.
Link to Textbook

Cohen, H. 2007. Complex Analysis with Applications in Science and Engineering. Springer, New York.
Link to Textbook

Ponnusamy, S. and Silverman, H. 2006. Complex Variables with Applications. Birkhauser, Boston.
Link to Textbook

Please see the references sections for other useful books.
References

Prerequisites

Math 324 used to be a prerequisite. Although we have dropped this prerequisite,
you should already know some vector algebra and multivariate calculus.
You should also be familiar with infinite series and Taylor expansions.

Grading

There will be a midterm and a final.
Exams constitute 60% of the final grade.
The final counts more than the midterm.
Homeworks count for 40% of your grade.

Calendar

Important Dates

September 25	-		Wednesday		-	First Lecture
October 28	-		Monday		-	Midterm
November 11	-		Monday		-	Veterans Day (No Class)
November 28	-		Thursday		-	Thanksgiving (No Class)
November 29	-		Friday		-	Thanksgiving (No Class)
December 6	-		Friday		-	Last Class
December 9	-		Monday		-	Final Exam (2:30-4:20 pm)

• Academic Calendar

• Final Exam Calendar

Videos

You may download videos of the lectures from this class's EDGE streaming video site

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

To read the EDGE student guide, please see EDGE student guide

Notes

• First-Day Handout

• Introduction
• Vector algebra
• Vector functions
• Vector fields
• Special coordinate systems
• Rate of change of vector fields
• Line integrals
• Surface integrals
• Stokes' theorem
• Volume integrals
• Complex algebra
• Analyticity
• Elementary functions
• Integration
• Power series
• Calculus of residues
• More residues
• Transforms
• Even more residues (optional)

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.

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

Young, E. C. 1993. Vector and Tensor Analysis. Marcel Dekker, 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. 2002. 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.

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.

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

Zill, D. G. and Shanahan, P. D. 2009. A First Course in Complex Analysis with Applications. Jones and Bartlett Publishers, Sudbury, MA.

Homework

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

• Homework #1
  Due: Wednesday, October 9, 2013
  hw1.pdf

• Homework #2
  Due: Wednesday, October 16, 2013
  hw2.pdf

• Homework #3
  Due: Wednesday, October 23, 2013
  hw3.pdf

• Stokes' Theorem & Divergence Theorem Practice Problems
  practice.pdf

• Homework #4
  Due: Friday, November 8, 2013
  hw4.pdf

• Homework #5
  Due: Friday, November 15, 2013
  hw5.pdf

• Homework #6
  Due: Monday, November 25, 2013
  hw6.pdf

• Homework #7
  Due: Monday, December 2, 2013
  hw7.pdf

• Homework #8
  Due: Friday, December 6, 2013 (Due in class for on-campus students)
  hw8.pdf

• Laplace Transform Practice Problems
  laplace.pdf