Syllabus
(Numerical Methods): Introduction to Matlab (or appropriate package)
and Numerical Computing: Number representations, finite precision
arithmetic, errors in computing.
Convergence, iteration, Taylor series. Solution of a Single Non-linear
Equation: Bisection method. Fixed point methods. Newton's method.
Convergence to a root, rates of convergence.
Review of Applied Linear algebra: Vectors and matrices. Basic
operations, linear combinations, basis, range, rank, vector norms,
matrix norms. Special matrices. Solving Systems of
equations (Direct Methods): Linear systems. Solution of triangular
systems. Gaussian elimination with pivoting. LU decomposition, multiple
right-hand sides. Nonlinear systems.
Newton's method. Least Squares Fitting of Data: Fitting a line to data.
Generalized least squares. QR decomposition. Interpolation:
Polynomial interpolation by Lagrange polynomials.
Alternate bases: Monomials, Newton, divided differences. Piecewise
polynomial interpolation. Cubic Hermite polynomials and splines.
Numerical Quadrature: Newton - Cotes Methods:
Trapezoid and Simpson quadrature. Gaussian quadrature. Adaptive
quadrature. Ordinary Differential Equations: Euler's Method. Accuracy
and Stability. Trapezoid method. Runge - Kutta method.
Boundary value problems and finite differences.
Reference Texts:
1. B. Kernighan and D. Ritchie: The C Programming Language
2. J. Nino and F. A. Hosch: An
Introduction to Programming and Object Oriented Design using JAVA
3. G. Recketenwald: Numerical Methods with Matlab
4. Shilling and Harries: Applied Numerical methods for
engineers using Matlab and C
5. S. D. Conte and C. De Boor: Elementary Numerical Analysis: An Algorithmic Approach
6. S. K. Bandopadhyay and K. N. Dey: Data Structures using C
7. J. Ullman and W. Jennifer: A first course in database systems
https://www.isibang.ac.in/~adean/infsys/database/Bmath/CS2.html
- Teacher: Mathew Joseph