# 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.