Course Archives: Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore

Course Archives Theoretical Statistics and Mathematics Unit

Course: Numerical Computing
Instructor: Soumyashant Nayak
Room: Second floor auditorium
Level: Undergraduate
Time: Currently offered

Syllabus
Past Exams

Syllabus:

i) INTRODUCTION TO OCTAVE (OR APPROPRIATE PACKAGE): Octave as a calculator, Built-in Variables and Functions, Functions and Commands; Creating Matrices, Subscript Notation for Matrix Elements, Colon Notation, Deleting Elements from Vectors and Matrices, Mathematical Operations with Matrices, Reshaping Matrices, Strings, Working with Data from External Files, Plotting.Script. Scripts m-Files; Function m-Files; Input and Output Parameters; Relational Operators, if...else..., Case Selection with switch , forLoops, whileloops, breakCommand, return Command; Vectorization.
ii) Number representations, finite precision arithmetic, errors in computing. Convergence, iteration, Taylor series.
iii) SOLUTION OF A SINGLE NON-LINEAR EQUATION: Bisection method. Fixed point methods. Newtons method. Convergence to a root, rates of convergence.
iv) 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.
v) LEAST SQUARES FITTING OF DATA: Fitting a line to data. Generalized least squares. QR decomposition.
vi) INTERPOLATION: Polynomial interpolation by Lagrange polynomials. Alternate bases: Monomials, Newton, divided differences. Piecewise polynomial interpolation. Cubic Hermite polynomials and splines.
vii) NUMERICAL QUADRATURE: Newton - Cotes Methods: Trapezoid and Simpson quadrature. Gaussian quadrature. Adaptive quadrature.
viii) ORDINARY DIFFERENTIAL EQUATIONS: Eulers Method. Accuracy and Stability. Trapezoid method. Runge - Kutta method. Boundary value problems and finite differences.

Reference Texts:

(a) B. Kernighan and D. Ritchie: The C Programming Language.
(b) J. Nino and F. A. Hosch: An Introduction to Programming and Object Oriented Design using JAVA.
(c) G. Recketenwald: Numerical Methods with Matlab.
(d) Shilling and Harries: Applied Numerical methods for engineers using Matlab and C.
(e) S. D. Conte and C. De Boor: Elementary Numerical Analysis: An Algorithmic Approach.
(f) S. K. Bandopadhyay and K. N. Dey: Data Structures using C.
(g) J. Ullman and W. Jennifer: A first course in database systems.

Evaluation: