Overview
Description
Norms of vectors & matrices, computation of eigen values and eigen vectors, matrix transformations, weierstrass’ approximation theorem, chebyshev polynomials, best and uniform approximation, splines, approximation in abstract spaces.
Units
Lecture3
Learning Outcomes
- demonstrate familiarity with the solution of numerical differential equations and understand the classification of PDEs using the terms parabolic, elliptic, and hyperbolic.
- study and explain partial differential equations such as Burger’s equation, the non-linear Schroedinger equation and the KdV equation using appropriate numerical algorithms such as Crank-Nicolson, ADI methods, upwind, implicit, explicit, Runge-Kutta, finite differences and psuedo-spectral methods.
- demonstrate understanding of concepts such as truncation error, stability, Fourier mode analysis, conserved quantities and dissipation.
- state and apply theorems such as the Lax equivalence theorem and the Peano kernel theorem.
- demonstrate understanding of algorithmic considerations related to parallel processing and write practical parallel computer programs.