{"product_id":"9789333218009","title":"Numerical Methods and Optimization  for SPPU 15 Course (TE - II - Mech. - 302047) (OLD EDITION)","description":"\u003cp\u003eUnit – I : Roots of Equation and Error Approximations  Roots of Equation Bisection Method, Newton Raphson method and Successive approximation method.  Error Approximations Types of Errors: 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 optimization: Newton’s Method. Modern Optimization Techniques: 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\/3rd Rule, Simpson’s 3\/8th Rule, Gauss Quadrature 2 point and 3 point method. Double Integration Trapezoidal rule, Simpson’s 1\/3rd Rule. (Chater - 9)\u003c\/p\u003e","brand":"Technical Publications","offers":[{"title":"Default Title","offer_id":46992947118372,"sku":"9789333218009","price":115.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0671\/3661\/8788\/files\/9789333218009_1.jpg?v=1694686030","url":"https:\/\/bookstation.in\/products\/9789333218009","provider":"BookStation","version":"1.0","type":"link"}