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