Content
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.