The important topics covered in this course are polynomial and piecewise polynomial (spline) interpolation, numerical integration and numerical differentiation, approximate solutions of differential equations, direct and iterative solution of a system of linear equations and eigenvalue problems.
The theory behind various methods is rigorously discussed. Emphasis is on comparison of various methods and their implementation using a computer.
Polynomial and piecewisepolynomial Interpolation:
Divided Difference, Lagrange and Newton Form
Some Basic Rules, Gaussian Integration, Composite Rules
Adaptive Quadrature, Romberg integration
Vector and Matrix Norms
Solution of System of Linear Equations:
Gauss Elimination Method, Partial Pivoting
Jacobi and GaussSeidel Methods
QR factorization using reflectors
Power Method and its variants:
Initial Value Problems:
Single step methods such as Euler's Method, RungeKutta
Methods, Taylor series method
Multistep methods such as AdamsBashforth method, Milne's method
PredictorCorrector Formula: AdamMoulton method
Boundary value problem:
Finite Difference method
Solution of nonlinear system of equations:
Basic Course in Calculus / Real Analysis
S. D. Conte and Carl de Boor, Elementary Numerical Analysis, An Algorithmic Approach, MacgrawHill International Editions, 1981.
K. E. Atkinson, An Introduction to Numerical Analysis, John Wiley &
Sons, paperback, 1989.
D. S. Watkins, Fundamentals of Matrix Computations, John Wiley & Sons, 1991
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