Course Archives    Theoretical Statistics and Mathematics Unit
Course: Computer Science II
Instructor: Siva Athreya
Room: Computer Class Room
Time: Currently offered
Syllabus
Past Exams

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

Evaluation:
 Midterm Exam 25 marks Assignment 25 marks Final Exam 50 marks Total 100 marks

Top of the page

Past Exams
Midterm
 03.pdf 07.pdf 09.pdf 10.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf
Semestral
 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf
Supplementary and Back Paper
 11.pdf 15.pdf 16.pdf 16S.pdf 17.pdf 18.pdf 19.pdf 19.pdf

Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]