Numerical Methods and Optimization for SPPU

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)

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