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B.Tech., , Electrical & Electronics Engineering, , MACX 04, , APPLIED NUMERICAL METHODS, , Regulations 2017, , L, , T, , P, , C, , 3, , 1, , 0, , 4, , OBJECTIVES:, The aims of the course are to, , , introduce basic computational methods for analyzing problems that arise in, engineering and physical sciences., , , , acquire knowledge about approximation theory and convergence analysis, associated with numerical computation., , MODULE I, , NUMERICAL SOLUTIONS OF EQUATIONS, , 7+3, , Bisection method - Regula Falsi method – Secant method - Fixed point iteration, method - Newton’s Raphson method –Gauss Elimination method - Gauss-Jordon, method – Gauss Jacobi method - Gauss-Seidel method., MODULE II, , INTERPOLATION, , 8+2, , Finite difference operators – Gregory Newton’s forward and backward, interpolations – Cubic spline interpolation - Lagrange interpolation - Newton’s, divided difference formula., MODULE III, , NUMERICAL DIFFERENTIATION AND INTEGRATION, , 8+2, , Numerical differentiation using Newton’s forward and backward formulae –, Numerical integration : Trapezoidal and Simpson’s 1/3 and 3/8 rules – Romberg’s, method – Gaussian Two Point and Three Point Quadrature formulae – Double, integrals using Trapezoidal and Simpson’s 1/3 rule., MODULE IV, , INITIAL VALUE PROBLEMS FOR FIRST ORDER, , 7+3, , ORDINARY DIFFERENTIAL EQUATIONS, Numerical solutions by Taylor’s Series method, Euler’s method, Modified Euler’s, Method - Runge – Kutta Method of fourth order – Milne’s and Adam’s Bashforth, Predictor and Corrector methods, MODULE V, , INITIAL AND BOUNDARY VALUE PROBLEMS FOR, , 8+2, , ORDINARY DIFFERENTIAL EQUATIONS, Numerical solutions by Taylor’s Series method - Runge – Kutta Method of fourth, order of second order ODE. Finite difference methods., , B.S. Abdur Rahman Crescent Institute of Science and Technology, , 319
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B.Tech., , Electrical & Electronics Engineering, , MODULE VI, , Regulations 2017, , BOUNDARY VALUE PROBLEMS FOR PARTIAL, , 7+3, , DIFFERENTIAL EQUATIONS, Finite difference solution of one dimensional heat equation by explicit and implicit, methods – One dimensional wave equation and two dimensional Laplace equation., L – 45; T – 15; Total Hours –60, TEXT BOOKS:, 1. Grewal, B.S., “Numerical methods in Engineering and Science”, 7th edition,, Khanna, Publishers, 2007., 2. C.F.Gerald, P.O.Wheatley, “Applied Numerical Analysis” ,Pearson Education,, New Delhi, 2002., REFERENCES:, 1. Chapra S.C, Canale R.P. “Numerical Methods for Engineers”, 5th Ed.,, McGraw Hill, 2006., 2. M.K.Jain, S.R.K.Iyengar, R.K.Jain, “Numerical methods for Scientific and, Engineering Computation”, New Age International Publishers, New Delhi,, 2003, OUTCOMES:, At the end of this course, students will be able to, 1. solve algebraic, transcendental and system of equations., 2. apply interpolation techniques., 3. carry out numerical differentiation and integration using different, methods., 4. solve first order ODE using single and multi step methods., 5. solve second order ODE, initial and boundary value problems., 6. solve the boundary value problems in PDE., , B.S. Abdur Rahman Crescent Institute of Science and Technology, , 320
