### MA5892 Numerical Methods & Scientific Computing

#### Course Details

– Part 0 Introduction, Root finding: Fixed point iteration (Newton method, Secant mathod, etc.)

– Part 1: Floating point arithmetic

– Part 2: Orthogonal polynomials, Polynomial Interpolation and Approximation

∗ Weierstrass approximation theorem

∗ Minimax approximation

∗ Computing the best approximation

∗ Lebesgue constants

∗ Error analysis

– Part 3: Numerical Differentiation

∗ Construction of finite difference schemes

∗ Pade Approximants

∗ Error analysis

∗ Non-uniform grids

– Part 4: Numerical Integration

∗ Rectangular, Trapezoidal and Simpsons rule

∗ Romberg integration and Richardson extrapolation

∗ Gaussian quadrature

∗ Adaptive quadrature

∗ Error analysis

– Part 5: Transform techniques

∗ Fourier, Laplace and Chebyshev transforms

∗ Fast algorithms for above

#### Course References:

– Approximation Theory and Approximation Practice, by Lloyd N. Trefethen

– Interpolation and Approximation by polynomials, by George M. Phillips