Syllabus - AS4 : Numerical Methods

AS4 :  Numerical Methods

( 4 Hours – 5 Credits)

UNIT I

Errors in computer Arithmetic –Empirical relations and Curve Fitting & Transcendental Equations:  Iteration method – Bisection method – Regula Falsi method – Newton Raphson method. 

UNIT II

Simultaneous Equations: Gauss elimination method –Gauss Jordan,  Gauss Seidel iteration methods.    

UNIT III

Interpolation: Newton’s interpolation formulae – Central difference interpolation formulae – Lagrange’s interpolation formula – Inverse interpolation. 

UNIT IV

Numerical differentiation: Newton’s Forward and Backward difference formulae – Numerical Integration: Trapezoidal rule – Simpson’s rule.    Eigen values and Eigen vectors of a matrix.     

UNIT V

Numerical solution of differential equations: Euler’s method – Taylor’s series method – Range-Kutta methods.    

Text book:

1. Numerical Methods,  T.   Veerarajan and T.   Ramachandran,  2^nd edition,  Tata McGraw Hill,  2006

Reference Books:

1. Numerical Methods by S.   Arumugam & A.   Thangapandi Issac,  A.   Somasundaram,  Sci Tech Publication,  Chennai,  2002. 

2.      Introductory Methods of Numerical Analysis,  S.  S.  Sastry,  Prentice Hall of India 

            Pvt.  Ltd,  New Delhi,   4th Edition,  2008.   

3.      Computer-Oriented Numerical Methods,  P.  Thangaraj,  Prentice Hall of India 

            Pvt.  Ltd,  New Delhi,  2008