**1. Introduction **

**2. Importance of numerical methods**

- Review of calculus
- Taylor’s theorem
- Errors in numerical computations
- Use of computer programming in numerical methods

**3. Solution of Nonlinear Equations**

- Nonlinear equations and their solutions
- Trial and error method
- Graphical method
- Iterative methods: Bisection method
- False position method
- Secant method
- Newton’s method
- Rate of convergence of iterative methods
- Newton’s method for polynomials and Horner’s rule

**4. Solution of Set of Algebraic Equations**

- Existence of solutions for linear set of equations
- Gaussian elimination method
- pivoting
- ill- conditioning
- Gauss-Jordan method
- Matrix inversion
- Matrix factorization: Doolittle algorithm
- Cholesky’s factorization
- Iterative solution using Gauss Seidel method
- Eigen value and eigen vector using power method

**5. Interpolation and Approximation**

- Newton’s interpolation using divided differences and difference table
- Cubic spline interpolation
- Least squares method of fitting linear and nonlinear function for given data

**6. Numerical Differentiation and Integration\**

- Numerical differentiation formulas
- Maxima and minima of a tabulated function
- Newton- Cote’s quadrature formulas: Trapezoidal
- Simpson’s 1/3 and 3/8 rule
- Romberg integration
- Gaussian integration

**7. Solution of Ordinary Differential Equations **

- Review of differential equations
- Initial value problem
- Taylor series method
- Euler’s method and its accuracy
- Henu’s method
- Runge-Kutta methods
- Solution of higher order equations
- Solution of boundary value problems using finite difference and Shooting method

**8. Solution of Partial Differential Equations **

- Review of partial differential equations
- Deriving difference equations
- Solution of Laplacian equation and Poisson’s equation