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Apr 19, 2024
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MATH 702 - Numerical Analysis and Approximation (3 units)
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 of Lecture: 3
Student Learning Outcomes
Upon completion of this course, students will be able to:
1. demonstrate familiarity with the solution of numerical differential equations and understand the classification of PDEs using the terms parabolic, elliptic, and hyperbolic.
2. 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.
3. demonstrate understanding of concepts such as truncation error, stability, Fourier mode analysis, conserved quantities and dissipation.
4. state and apply theorems such as the Lax equivalence theorem and the Peano kernel theorem.
5. demonstrate understanding of algorithmic considerations related to parallel processing and write practical parallel computer programs.
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