First-order ODEs: separable, linear, exact, Bernoulli's equation, and applications.
Higher-order linear ODEs with constant coefficients, method of undetermined coefficients, variation of parameters.
Laplace transforms, inverse transforms, properties, and solution of ODEs using Laplace transforms.
Analytic functions, Cauchy-Riemann equations, complex integration, Cauchy's integral theorem and formula.
Numerical solutions of algebraic and ODE systems: Newton-Raphson, interpolation, Euler, and Runge-Kutta methods.