Unit 1

Solution of Nonlinear Equations: Bisection and False position Methods, Newton Raphson and Secant Methods, Rate of Convergence.

Unit 2

Solution of Linear Systems AX=B and Eigen value problems (12 hours): Direct methods, Gaussian Elimination, Gauss Jordan method, LU Factorisation, Jacobi & Gauss Seidel iterative Methods.

Unit 3

Interpolation, Curve Fitting (12 hours): Taylor’s Series calculation of Functions, Lagrange’s Polynomial Approximation and Interpolation, Newton Polynomial Approximation using divided differences and Interpolation, Error, Newton-Gregory forward and backward difference interpolation, Hermite interpolation, Piecewise and Spline interpolation, Polynomial approximation and Weierstrass theorem, Principle of Least Squares.

Unit 4

Numerical Differentiation and Integration (10 hours):Numerical Differentiation using Lagrange, Finite difference interpolation and Undetermined coefficient method, Numerical Integration using Newton-Cotes method, Gauss-Legendre Integration method, Trapezoidal and Simpson method, Quadrature, Composite Trapezoidal and Simpson’s Rule, Romberg Integration, Orthogonal polynomials and Gaussian integration.

Unit 5

Solution of Ordinary Differential Equations (10 hours): Euler method,Modified-Euler mid-point method, Taylor series method, Runge-Kutta methods, Error analysis.

Lab Exercises to be done Using Python

1. Bisection and False position Methods.
2. Newton Raphson and Secant Methods.
3. Gaussian Elimination, Gauss Jordan method, LU Factorization
4. Iterative Methods for Solving Linear Equations.
5. Polynomial Approximation and Interpolation Methods 1
6. Polynomial Approximation and Interpolation Methods 2
7. Numerical Differentiation.
8. Numerical Integration 1.
9. Numerical Integration

Bisection and False position Methods.
Newton Raphson and Secant Methods.
Gaussian Elimination, Gauss Jordan method, LU Factorization
Iterative Methods for Solving Linear Equations.
Polynomial Approximation and Interpolation Methods 1
Polynomial Approximation and Interpolation Methods 2
Numerical Differentiation.
Numerical Integration 1.
Numerical Integration

Course Outcome:
CO-1: Understand the basic concepts of root finding methods, system of equations and their solutions.
CO-2: Understand the concepts of interpolation and construction of polynomials.
CO-3: Application of numerical methods to understand the concept of Calculus (Differentiation and Integration).
CO-4: Application of numerical concepts to solve ODEs and PDEs. CO-5: Usage of software tools to solve various problems numerically.

1. Jain M.K., Iyengar S.R.K. and Jain R.K., Numerical Methods for Engineering and Scientific
2. Computation, 3rd edition, New Age International (P), New Delhi, 1995. References:
3. John H. Mathews, Kurtis D. Fink, Numerical Methods Using Matlab, 4th edition, Prentice-Hall.
4. Rudra Pratap, Getting Started with MATLAB 7: A Quick Introduction for Scientists and Engineers, Oxford University Press, 2005.