Computational Topics

Computational and Data Sciences Applied to National Security and Nuclear Engineering Topics

Numerical Methods

1. Gauss Elimination
2. LU Factorization
3. Basic Iterative Solvers (Jacobi and Gauss Seidel)
4. Round-off error and finite precision arithmetic
5. Interpolation (Lagrange polynomials and cubic splines)
6. Basic curve fitting (linear regression)
7. Quadrature techniques (Newton-Coates rules and Gaussian quadrature)
8. Finite Difference Methods 9
9. Convergence and order of accuracy
10. Time integration techniques (forward and backward Euler, Crank-Nicolson, RungeKutta)
11. Stability of numerical methods
12. Eigenvalue problems and solution techniques (power iteration, inverse power iteration)

Monte Carlo Methods

1. Cumulative Distribution Function
2. Probability Density Functions
3. Sampling from a distribution (inverting the Cumulative Distribution Function and rejection sampling)