Preliminaries: Introduction to MATLAB, numerical errors, interpolation, curve fitting, spectral analysis
Ordinary Differential Equations: Introduction to basic, runge kutta and adaptive methods.
Systems of equations: Linear equations, nonlinear equations, iterative solutions to matrix equations
Partial differential equations: Solutions to parabolic and elliptic equations using finite difference methods, solutions to hyperbolic equations using finite difference andlimiters, stability analysis, implicit methods.
Optional: Introduction to Mathematica, examples from orbital mechanics - analytic solutions and numerical solutions, special functions, quadrature, stochastic methods, (depending on class interest)
All information is representative only, and is likely to change from year to year.