- Ordinary differential equations; power series solution, Legendre’s equation, Bessel equation. Laplace transform: convolution theorem; application to simple initial value problems and integral equations; periodic function.
- Fourier series: Euler’s formulae; even and odd functions; half range expressions; solutions to some ordinary differential equations.
- Partial differential equation: classification; tehone-dimension wave equation, the heat conduction and diffusion equation; Laplace’s equation in cylindrical and spherical polar coordinates.
- Vector calculus: scalar and vector fields; vector calculus; curves; arc length, tangent, curvature and torsion; directional derivatives, divergences and curl of a vector field; line integrals; surface integrals; Stoke’s theorem and divergence theorem.