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Numerical Analysis

Basic Topics

Course material-Mathematics 151AB and 269A.

Topics

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.