Numerical Methods (MA207)
Course Name:
Numerical Methods
Programme:
B.Tech(Civil)
Semester:
Third
Category:
Programme Core (PC)
Credits (L-T-P):
(3-0-0) 3
Content:
Root finding of polynomials (zeros of a function) and transcendental functions (nonlinear equation), bracketing, bisection, secant, and Newton Raphson methods. Interpolation, splines, polynomial fits, Chebyshev approximation.
Numerical Integration and Differentiation: Evaluation of integrals, elementary analytical methods, trapezoidal and Simpson’s rules, Romberg integration, Gaussian quadrature and orthogonal polynomials, multiple integrals, improper integrals, summation of series, Euler-Maclaurin summation formula, numerical differentiation and estimation of errors. Linear system of equations, LU factorization, Special types of Matrices, Iterative Methods – Jacobi, Gauss-Siedel, SOR methods.
Course Outcomes:
References:
1) Richard L. Burden and J. Douglas Faires, Numerical Analysis: Theory and Applications, India Edition, Cengage Brooks-Cole Publishers, 2010.
2) W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C/FORTRAN, Prentice Hall of India, New Delhi, 1994.
3) Jaan Kiusalaas, Numerical Methods in Engineering with MATLAB, 2nd Edition, Cambridge University Press, 2009.
Department:
Mathematical and Computational Sciences