Course material-Mathematics 151AB and 269A.
Interpolation and approximation: divided differences, Chebycheff systems, Lagrangian interpolation, splines; numerical differentiation and integration: elementary quadrature, Simpson’s, Gauss’s and Romberg’s rules; solutions of nonlinear equations: Newton’s method and its variations, estimate of rate of convergence; error analysis: methods of approximation of round-off errors and fixed and floating point arithmetic; numerical methods in Linear Algebra: Gaussian elimination, diagonalization of symmetric matrices, conditioning; numerical methods for ordinary differential equations; initial value problems, 2 point boundary value problems and eigenvalue problems; introduction to numerical methods for partial differential equations.
More Adavanced Topics
Course material- Mathematics 151 AB and 269ABC.
Difference methods for time dependent problems: stability, consistency, convergence, initial boundary value theory, and nonlinear problems; finite element methods; initial and boundary value problem, approximation theory, linear algebra considerations.
References – Basic Level
- Conte and de Boor (1980). Elementary Numerical Analysis (3rd edition,) McGraw Hill.
- Dahlquist and Bjorck (1974). Numerical Methods, Prentice Hall.
- Henrici (1964). Elements of Numerical Analysis, Addison Wesley.
- Ralston, J. (1965). A First Course in Numerical Analysis, McGraw Hill.
References – More Advanced Topics
- Johnson (1987), Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge U. Press.
- Kreiss and Oliger (1973), Methods for the Approximate Solution of Time Dependent Problems, Garp.
- Richtmyer and Morton (1967), Difference Methods for Initial- Value Problems, Wiley.
- Sod (1985), Numerical Methods in Fluid Dynamics, Cambridge U. Press.