Monte Carlo method: Definition and implementation.
Random numbers ? requirements. Types of random number generators. Tests.
Probabilities: discrete, continuous and cumulative. Uniform distribuition. Non-uniform distributions: exponential and Gaussian.
Change of probability density: inversion and Box-Muller methods. Change of variables.
Monte Carlo integration.
Finding the root of equations: successive substitutions, Newton-Cotes, half intervals and regula-falsi methods.
Interpolation methods: polynomial interpolation, Lagrange formula and piecewise interpolation.
Finding the roots of functions: Newton-Raphson, secant, bisection and regula-falsi
Integration methods: Newton-Cotes quadrature (open and closed), middle point, trapezoid and Simpson rules. Gaussian quadrature.
Integration of differential equations: Euler, Neuer and Runge-Kutta methods.
Random walks, Markov chains, Metropolis algorithm. Examples and applications.
Bibliography of reference
- Knuth, The Art of Computer Programming, 3rd vol, Addison-Wesley, 1999.
- Press et al., Numerical Recipies in c, Camb. Univ. Press, 1992.
- Wong, Computational Methods in Physics and Engineering, 2nd ed, Prentice-Hall, 1997.
- R. Gaylord, P. Wellin, Computer Simulations with Mathematica, Springer, 1995.