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AMATH 401 A: Vector Calculus and Complex Variables

Meeting Time: 
MTWF 2:30pm - 3:20pm
LOW 205

Syllabus Description:

Grading will be based on homework and exams. Homework will count for 40% of the final grade, the midterm 20%, and the final 40%. Homeworks will be set on Fridays and are due the following Wednesday.

There are no required texts: the lecture notes will be self-contained. Several texts are recommended as being useful, but are not required to pass the course with a good grade.

Weeks 1-4 will be spent on vector calculus, and weeks 5-10 on complex analysis. The content of these lectures will be as follows:

  1. Orthogonal coordinate systems, Jacobians, and scale factors
  2. Grad, div and curl
  3. Line, surface, and volume integrals
  4. Integral theorems
  5. Complex functions and analyticity
  6. Integration and Morera’s theorem
  7. Cauchy’s theorem and integral formula
  8. Taylor series and Laurent series
  9. Residues and contour integration
  10. Fourier and Laplace transforms

Lectures will contain worked examples which the students will discuss.

Catalog Description: 
Emphasizes acquisition of solution techniques; illustrates ideas with specific example problems arising in science and engineering. Includes applications of vector differential calculus, complex variables; line-surface integrals; integral theorems; and Taylor and Laurent series, and contour integration. Prerequisite: either MATH 126 or MATH 136. Offered: A.
GE Requirements: 
Natural World (NW)
Last updated: 
October 17, 2018 - 9:00pm