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.