Course Archives    Theoretical Statistics and Mathematics Unit
Course: Computer Science II
Level: Undergraduate
Time: Currently not 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

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

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