Course Outline


1.Introduction to Numerical Computation - Mistakes, errors, rounding, and truncation errors

2.Computer Arithmetic - Floating point numbers, range, precision, EPS

3.Linear Systems - Matrix formulation, sparse and stored matrices, Gaussian elimination, partial pivoting, iterative methods, Gauss-Seidel method, sparse matrix storage

4.Finite Differences Taylor Series, tables, effect of errors

5.Interpolation - Definition of the problem, difference formulae, Lagrange interpolation, cubic splines

6.Numerical Differentiation and Integration - Problems with differentiation, Trapezoidal and Simpson formulae, interval halving, h^2 extrapolation, Gaussian quadrature and related formulae

7.Root Finding - Bisection, secant, Newton methods and extensions

8.Linear Least Squares - Exploring data, normal equations, orthogonal transformations

9.Ordinary Differential Equations - Initial and boundary value problems, Euler and Runge-Kutta methods, Multi-step methods