Ordinary differntial equations: First-order differential equations ; Linear differential equarions of second and higher order ; Systems of differential equations, phase plane, qualitative methods ; Series solutions of differential equations. Special functions ; Laplace transforms -- Linear algebra, vector calculus: Linear algebra: matrices, vectors, determinants. Linear systems of equations ; Linear algebra: matrix eigenvalue problems ; Vector differential calculus, Grad, Div, Curl ; Vector integral calculus. Integral theorems -- Fourier analysis and partial differential equations: Fourier series, integrals, and transforms ; Partial differential equations -- Complex analysis: Complex numbers and functions. Conformal mapping ; Complex integration ; Power series, Taylor series ; Laurent series, residue integrationn ; Complex analysis applied to potential theory

1. Mathematical physics
2. Engineering mathematics