PHY422: Computational methods in physics I

        [Cr:4, Lc:3, Tt:0, Lb:3]

Course Outline

• Number representation in computers, round off error, relative error estimation, error propagation.
• Solution of Linear Systems $AX=B$: Matrix arithmetic, Numerical Diagonalization of matrices. Singular value decomposition. Eigenvalue problem. Gaussian Elimination, $LU$ Factorization, Jacobi and Gauss-Seidel method, Error estimation and Residual Correction method.
• Interpolation: Polynomial interpolation, Newton, Lagrange and Hermite interpolation, spline interpolation.
• Numerical Differentiation: Differentiation of interpolating polynomials, Backward, forward and centered difference methods, method of undetermined coefficients.
• Numerical Integration: Trapezoidal and Composite Trapezoidal, Simpson's Rule, Gaussian quadrature, Monte Carlo Integration.
• Solution of Nonlinear Equations $f(x)=0$: Iteration, Bracketing methods for locating a root, Newton-Raphson and Secant methods.
• Optimization: Minimization, minimization in several dimensions, Monte Carlo Markov Chains based methods. Metropolis method, convergence of Markov Chains.

Recommended Reading

• H. M. Antia, Numerical Methods For Scientists And Engineers, 02nd edition, Birkhauser Basel (2002).
• Numerical Recipes in C: The Art of Scientific Computing, W. H. Press, S. A. Teukolsky, W. T. Vellerling and B. P. Flannery, Cambridge University Press (1992).