MEHRAN UNIVERSITY OF ENGINEERING AND TECHNOLOGY, JAMSHORO DEPARTMENT OF BASIC SCIENCES AND RELATED STUDIES Title of Subject
:
Numerical Methods and Computations
Name of Teacher
:
Muhammad Mujtaba Shaikh (
[email protected] )
Marks : 100
Discipline Pre-requisites
: :
Assessment Credit Hours
: :
12MT (5th Term) Intermediate Mathematics, Applied Calculus, Linear Algebra, Differential Equations 20% Sessional work, 80% Written examination Theory (04) + Practical (02) Minimum Contact Hours : 52 + 26
Aims Objects
: To introduce the concept of numerical methods and computations. : After completion of this course, the student should be familiar with: Root of a non-linear equation f (x) = 0 and its numerical computation. Iterative methods for the solution of linear algebraic system of equations. Interpolation and extrapolation. Numerical differentiation and integration. Numerical solution of ordinary and partial differential equation. Contents : Error Analysis: Introduction, floating points, errors, types of errors. Solution of Non-Linear Equations: Bisection method, Regula-Falsi method, Newton-Raphson method for one and two variables, Fixed-point iterative method. Solution of Linear System of Algebraic Equations: Direct methods: Doolittle’s, Crout’s and Choleskey methods. Iterative methods: Jacobi’s method, Gauss-Seidel method. Eigen values and Eigen vectors: Characteristic equation method, Power’s method. Interpolation and Extrapolation: Differences: Forward, backward, central, operators and their relations. Newton’s forward interpolation formula, Newton’s backward interpolation formula, Newton’s divided difference formula, Lagrange’s interpolation formula, Stirling’s formula. Numerical Differentiation: Newton’s forward and backward differentiation formulae, etc. Numerical Quadrature: Trapezoidal rule, Simpson’s one-third rule, Simpson’s three-eighth rule, Gaussian quadrature. Numerical Solution of Ordinary Differential Equations: Taylor Series method, Picard’s method, Euler’s and its modified methods, Runge-Kutta methods, MilineySimpson’s method, Adam-Moulton’s method (Predictor corrector) Solution of Higher Order Differential Equations: Runge-Kutta methods. Numerical Solution of Partial Differential Equations: Finite difference method, Explicit method, Implicit method, Crank-Nicholson method, ADI method. Books Recommended: Canal and Chapra, Numerical methods for Engineers Curits F. Gerald, Applied Numerical Analysis Evvien Cryzigg, Advance Engineering Mathematics Chung Yau lam, Applied numerical methods for the solution of partial differential equations. Dr. Saeed Akhter Bhatti, A first course in numerical analysis. John L. Van Iwaarden, Ordinary differential equations with numerical techniques. _________________________________________________________________________________ Study Material: http://shaikhmuhammadmujtabakhan.blogspot.com/p/study-material-for-my-students-at-muet.html
