Contents:

This course deals with how functions, derivatives, integrals, matrices and differential equations are evaluated as strings of numbers in the computer. It studies the speed of convergence of Taylor, Fourier, and other series expansions and their utility. Applications of these techniques in solving model engineering problems are included. Finally, it expects the students to write a computer program for several of the numerical techniques covered in the course.

Lecturewise Breakup (based on 50min per lecture)

I. Concepts of Algorithms and Programming; Revision of computer languages such as MATLAB, Fortran, and
    C++ (2 Lectures)

II. Introduction to Mathematical Modelling (3 Lectures)

III. Taylor and Fourier series expansion (3 Lectures)

IV. Root finding (3 Lectures)

V. Interpolation, splines, extrapolation (3 Lectures)

VI. Regression and curve fitting (2 Lectures)

VII. Solution of simultaneous linear algebraic systems; nonlinear algebraic equations (5 Lectures)

VIII. Eigenvalues and eigenvectors (2 Lectures)

IX. Solution of simultaneous non-linear algebraic systems (1 Lecture)

X. Numerical integration, Simpson’s rule, Gaussian quadrature (3 Lectures)

XI. Solution of ODE: R. K. Methods; Predictor-Corrector methods; boundary-value problems (5 Lectures)

XII. Systems of ODE’s; convergence and error studies (4 Lectures)

XIII. Linear PDEs by finite differences (4 Lectures)

Programming projects based on mathematical modelling followed by an application of the numerical methods given above ( ~ 20% weightage)

References:

1. Numerical Methods for Engineers; Steven C. Chapra and Raymond P. Canale, 7th edition, McGraw-Hill, 2014.

2. Introduction to Numerical Analysis, S.S. Sastry; Prentice Hall of India,  2012.

3. Numerical Methods for Engineers, Santhosh .K. Gupta, New Age International; 2012.

4. Applied Numerical Methods for Digital Computation , M.L. James, G.M. Smith & J.C. Wolford, Harper- Collins College Division; 4th edition, 1993.