The course will introduce students to the art of numerical computation. The theory and derivation of computational techniques, error analysis, practical implementation and limitations will be covered in this course.
Module 1: Error AnalysisAccuracy; machine precision; Truncation and round-off errorsModule 2: Linear Systems and EquationsEigenvalues; Gauss elimination, TDMA, LU decomposition; Gauss-Siedel method, over-relaxation;derivation/applications thereofModule 3: Numerical differentiationDifferentiation, derivation of various formulae, round-off / truncation error tradeoffModule 4: Numerical integrationNewton-cotes formulae, error analysis; Richardson’s methodModule 5: Nonlinear Algebraic EquationsBracketing methods: bisection and regula-falsi;Open methods: Newton-Raphson, fixed point iteration, Secant; Error analysis for various methods;Root finding; Practical implementationModule 6: RegressionLinear regression; regression in multiple variables; regression of some functional formsModule 7: Ordinary Differential Equations (ODE) Euler’s implicit and explicit methods; stability;Runge-Kutta methods and derivation; Adam Moulton and Predictor-Corrector methods;Multi-variable ODEs; Stiff Systems; ODE – Boundary Value ProblemsModule 8: Partial Differential EquationsClassification of partial differential equations; finite difference technique; Method of lines
1. Gupta S.K. (1995) Numerical Methods for Engineers, New Age International2. Chapra S.C. and Canale R.P., Numerical Methods for Engineers, 6th Ed., McGraw Hill3. Fausett L.V. (2007) Applied Numerical Analysis Using MATLAB, 2nd Ed., Pearson Education
1. Numerical Recipes in C