**[Cr:4, Lc:3, Tt:0, Lb:3]**

- Number representation in computers, round off error, relative error estimation, error propagation.
- Solution of Linear Systems : Matrix arithmetic, Numerical Diagonalization of matrices. Singular value decomposition. Eigenvalue problem. Gaussian Elimination, 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 : 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.

- 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).