June 23, 07

MA 214: Introduction to Numerical Analysis  (3-1-0-8)
Interpolation of polynomials, divided differences, error of the
interpolating polynomial, piecewise linear and cubic spline interpolation.
Numerical integration, composite rules, error formulae.
Solution of a system of linear equations, implementation of Gaussian
elimination, Gauss-Seidel methods, partial pivoting, row echelon form, LU
factorization Cholesky's method, ill-condition, norms.
Solution of nonlinear equation, bisection and secant methods.
Newton's method, rate of convergence, solution of a system of nonlinear
equations, numerical solution of ordinary differential equations, Euler and
Runge-Kutta methods, multi-step methods, predictor-corrector methods, order
of convergence, finite difference methods, numerical solutions of elliptic,
parabolic and hyperbolic partial differential equations.
Eigenvalue problem, power method, QR method, Gershgorin's theorem. Exposure
to software packages like IMSL subroutines, MATLAB.

Text/References
1. S. D. Conte and Carl de Boor, Elementary Numerical Analysis- An
Algorithmic Approach, 3rd ed., McGraw-Hill, 1980.
2. C. E. Froberg, Introduction to Numerical Analysis, 2nd ed.,
Addison-Wesley, 1981.
3. E. Kreyszig, Advanced Engineering Mathematics, 8th ed., John Wiley, 1999.