Computational Methods in Engineering

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Description

This course provides an introduction to the numerical methods to solve various kinds of equations that students encounter in the field of engineering. The student will develop his/her own programs/subroutines for the numerical schemes taught in the course.

Course Contents

Numerical Methods in Linear Algebra:Direct and iterative solution techniques for simultaneous linear algebraic equations – Gauss elimination, Gauss-Jordon, LU Decomposition, QR Method, Jacobi and Gauss-Seidel MethodsEigenvalues and Eigenvectors – Power and inverse power method, householder transformation, physical interpretation of eigenvalues and eigenvectorsSolution of nonlinear algebraic equations: Bisection method, fixed-point iteration method, Newton-Raphson, Secant method, solution of system of nonlinear algebraic equationsInterpolation: Polynomial interpolation, Lagrange interpolating polynomial, Hermite interpolation, interpolation in 2 and 3 dimensionsNumerical Differentiation and IntegrationFinite difference formula using Taylor series, Differentiation of Lagrange polynomials, Simpson’s rule, Gauss-quadrature rule, Romberg method, multiple integralsNumerical solution of differential equationsOrdinary Differential Equations – Euler, Heun’s method and Stability criterion, second order and fourth order Runge-Kutta methods, Adams-Bashforth-Moulton method, system of ODEs and nonlinear ODEsPartial Differential Equations – Classification of PDEs, Elliptic equations, Parabolic equations (Transient diffusion equation), Hyperbolic equations (wave equation)

Text/Reference Books

1. S. P. Venkateshan, Prasanna Swaminathan, Computational Methods in Engineering, Ane Books
2. Steven C. Chapra, Numerical Methods for Engineering, Mc-Graw Hill Education
3. Joe D Hoffman, Numerical Methods for Engineers and Scientists, Second Edition, Marcel Dekker (2001)
4. Gilbert Strang, Computational Science and Engineering, Wellesley-Cambridge Press