Numerical and Statistical Methods in Chemistry 1200-1MNUMWZ

1. Introduction: floating-point arithmetic, numerical errors, stability of algorithms, computational scaling with the input size.
2. Numerical linear algebra: LU decomposition of a square matrix and its application to systems of linear equations.
3. Finding eigenvalues and eigenvectors of real matrices.
4. Numerical differentiation: finite-difference formulas for the first and second derivatives. Application to linear differential equations.
5. Numerical integration.
6. Monte Carlo method for numerical integration in many dimensions.
7. Interpolation with help of Lagrange and Chebyshev polynomials, Runge's phenomenon. The approximation problem, least-squares method.
8. Numerical solutions of nonlinear equations, finding roots of high-order polynomials, minimization of functions in one dimension (golden-section search).
9. Numerical methods for solving ordinary differential equations (Euler method, Runge-Kutta method).
10. Minimization problem in many dimensions, the local minima problem.
Some of the above items are optional.