Numerical Methods and Application of Matlab

Paper Code: 
PHY 222
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

The student will learn C++ language and MATLAB to the extent, she can apply these techniques to problem solving in Physics, pertaining to P.G. Programme and research.

Unit I: 

Errors in Numerical Analysis: Source of Errors, Round off error, Arithmetic error, error analysis, Condition and stability,  method of undetermined coefficients, use of interpolation formula, iterated interpolation, inverse interpolation, Hermite interpolation and Spline interpolation(linear method).

Unit II: 

Solution of Linear equations : Direct and Iterative methods, Jacobi and Gauss Seidal method

Solution of Nonlinear equation: Bisection method,

Newton-Raphson method, Generalized Newton Raphson method, method of iteration, Newton Raphson method for the case of nearly equal roots, double root and multiple roots.

Unit III: 

Integration of a function: Trapezoidal and Simpson's rules. Gaussian quadrature formula, Singular integrals, Double integration.

Integration of Ordinary differential equation: Predictor-corrector methods, Runga-Kutta method. Simultaneous and Higher order equations.

Numerical differentiation of Data, Least-Squares Approximations, Fast Fourier Transformation.

Unit IV: 

Curve fitting using MATLAB: Least square line, Methods of curve fitting, Interpolation by Spline functions, Fourier series and trigonometric polynomials, Bezier curve

 

Unit V: 

Numerical Integration using MATLAB: Introduction to Quadrature, Composite trapezoidal and Simpson’s Rule, Recursive rules, Adaptive Quadrature, Gauss-Legendre Integration

 

References: 
  1. “A First Course in Numerical Analysis”, A Ralston and P. Rabinowitz, McGraw Hill (1985).
  2. “ Introductory Methods of Numerical Analysis”, S.S. Sastry, Prentice-Hall of India (1979).
  3. “Numerical Methods using MATLAB.”, John H. Mathews and Kurtis D. Fink, PHI

 

 

 

Academic Year: 
2015-2016
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