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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)