Introduction to Numerical Analysis

Measuring Errors

Sources of Errors

Propagation of Errors

                  Solution of Nonlinear Equations

                   Bisection Method

                   Newton Raphson Method

                   Secant Method

                   False Position Method

                Regression and Interpolation

                Linear Regression

                Nonlinear Regression

              Adequacy of Regression

              Direct Method Interpolation

              Newton’s Method of Interpolation

              Lagrange Interpolation

               Spline Interpolation

           Numerical Differentiation and Integration

            Numerical Differentiation

           Continuous Functions

           Discrete Functions

           Numerical Integration

           Trapezoidal Rule

           Simpson’s  Rule

           Gauss Quad Rule

           Improper Integrals

Initial Value Problems for Ordinary Differential Equations

Elementary Theory of Initial Value Problems

Euler’s Method

Finite Differential Method

Runge Kutta Methods

Shooting Method

Higher Order Differential Equations

Numerical Optimization

Golden Section Search Method

Newton’s Method

Direct Search Method

Gradient Search Method

Simplex Method

Recommended Books:

1.   Numerical Analysis by Richard L. Burden

2.   Numerical Methods with Applications by Autar K. Kaw

Course Material