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:
- Orthogonal coordinate systems, Jacobians, and scale factors
- Grad, div and curl
- Line, surface, and volume integrals
- Integral theorems
- Complex functions and analyticity
- Integration and Morera’s theorem
- Cauchy’s theorem and integral formula
- Taylor series and Laurent series
- Residues and contour integration
- Fourier and Laplace transforms
Lectures will contain worked examples which the students will discuss.