Numerical Methods and Optimization for SPPU 15 Course (TE - II - Mech. - 302047) - 2020 Edition

by Anup Goel

Unit – I : Roots of Equation and Error Approximations Roots of Equation Bisection Method, Newton Raphson method and Successive approximation method. Error Approximations Types of Absolute, Relative, Algorithmic, Truncation, Round off Error, Error Propagation, Concept of convergence-relevance to numerical methods. (Chapters - 1, 2) Unit – II : Simultaneous Equations Gauss Elimination Method with Partial pivoting, Gauss-Seidal method and Thomas algorithm for Tri-diagonal Matrix, Jacob iteration method. (Chapter - 3) Unit – III : Optimization Introduction to optimization, Classification, Constrained optimization (maximum two constrains): Graphical and Simplex method, One Dimensional unconstrained Newton’s Method. Modern Optimization Genetic Algorithm (GA), Simulated Annealing (SA). (Chapter - 4) Unit – IV : Numerical Solutions of Differential Equations Ordinary Differential Equations [ODE] Taylor series method, Euler Method, Runge-Kutta fourth order, Simultaneous equations using RungeKutta order method. Partial Differential Equations [PDE] : Finite Difference methods Introduction to finite difference method, Simple Laplace method, PDEs- Parabolic explicit solution, Elliptic-explicit solution. (Chapters - 5 and 6) Unit – V : Curve Fitting and Regression Analysis Curve Fitting Least square technique - Straight line, Power equation, Exponential equation and Quadratic equation. Regression Analysis Introduction to multi regression analysis, Lagrange’s Interpolation, Newton’s Forward interpolation, Inverse interpolation (Lagrange’s method only). (Chapters - 7, 8) Unit – VI : Numerical Integration Numerical Integration (1D only) Trapezoidal rule, Simpson’s 1/ Rule, Simpson’s 3/ Rule, Gauss Quadrature 2 point and 3 point method. Double Integration Trapezoidal rule, Simpson’s 1/ Rule. (Chapter - 9)

Kindle Edition

Published May 3, 2020