First and Second Order ODE's. Systems of ODE's. Linear Algebra, solving linear systems by Gaussian elimination, inverting matrices by Gauss-Jordan elimination. Elgenvalues, Eigenvectors. Vector Differential and Integral. Calculus, including the three major theorems (Gauss Divergence, Green's and Stokes'). Fourier Series, Integral and Transform. Complex numbers, Cauchy-Riemann equations, analytic functions.