AMATH 401

Vector Calculus and Complex Variables
Fall 2007

Schedule

SLN:		10201
Days:		M, T, W, F
Time:		1:30-2:20 pm
Room:		Loew 216

• Current Section Status

Instructor

Name:		Mark Kot
Office:		415G Guggenheim Hall
Phone:		(206) 543-0908
Fax:		(206) 685-1440
Email:		kot@amath.washington.edu

Office Hours:		M, W, F
		3:00-4:00 pm

• Personal Web Page

Assistants

Name:		Mingyuan Zhong
Office:		Guggenheim 407
Phone:		(206) 685-1440
Fax:		(206) 685-8069
Email:		zhongmy@amath.washington.edu

Office Hours:		Tuesday 9:30-10:30 am (in 415L)
		Wednesday 9:00-10:00 am (in 415L)
		Thursday 1:30-2:30 pm (in 415L)

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

Recommended:

• Cooray, T. M. J. A. 2006.
  Complex Analysis with Vector Calculus
  Alpha Science, Oxford, UK

University Book Store

• Textbook Status

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 26	-		Wednesday		-	First Lecture
October 29	-		Monday		-	Midterm
November 12	-		Monday		-	Veterans Day (No Class)
November 22	-		Thursday		-	Thanksgiving (No Class)
November 23	-		Friday		-	Thanksgiving (No Class)
December 7	-		Friday		-	Last Lecture
December 10	-		Monday		-	Final Exam (2:30-4:20 pm)

• Academic Calendar

• Final Exam Calendar

Videos

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

To read more about streaming video see the EDGE information page

Notes

• 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)

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 10, 2007
  hw1.pdf

• Homework #2
  Due: Wednesday, October 17, 2007
  hw2.pdf

• Homework #3
  Due: Wednesday, October 24, 2007
  hw3.pdf

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

• Homework #4
  Due: Friday, November 9, 2007
  hw4.pdf

• Homework #5
  Due: Friday, November 16, 2007
  hw5.pdf

• Homework #6
  Due: Tuesday, November 27, 2007
  hw6.pdf

• Homework #7
  Due: Monday, December 3, 2007
  hw7.pdf

• Homework #8
  Due: Friday, December 7, 2007 (Due in-class for on-campus students!)
  hw8.pdf