Calculus covers vector calculus and complex variables in 2 sections spanning 13 lectures.
Section 1: Vector Calculus
- Calculus of vector-valued functions
- Arc length, space curves, and curvature
- Triple integrals
- Triple integrals in other coordinate systems and transformations
- Vector fields, differential operators, and line integrals
- Green’s theorem and surface integrals
- Stokes’ theorem and the divergence theorem
Section 2: Complex Variables
- Limits and differentiation of functions of a complex variable
- Analytic functions, Cauchy-Riemann equations, and harmonic functions
- Singularities and complex integration
- Complex integration, Taylor and Laurent series
- Singularities and residue theory
- Applications of residues to real integrals