*UNIT I* SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS

Solution of algebraic and transcendental equations

Fixed point iteration method

Newton Raphson method

Solution of linear system of equations

Gauss elimination method

Pivoting

Gauss Jordan method

Iterative methods of Gauss Jacobi and Gauss Seidel

Eigenvalues of a matrix by Power method and Jacobi’s method for symmetric matrices.

*UNIT II* INTERPOLATION AND APPROXIMATION

Interpolation with unequal intervals

Lagrange’s interpolation

Newton’s divided difference interpolation

Cubic Splines

Difference operators and relations

Interpolation with equal intervals

Newton’s forward and backward difference formulae.

*UNIT III* NUMERICAL DIFFERENTIATION AND INTEGRATION

Approximation of derivatives using interpolation polynomials

Numerical integration using Trapezoidal,

Simpson’s 1/3 rule

Romberg’s Method

Two point and three point Gaussian quadrature formulae

Evaluation of double integrals by Trapezoidal and Simpson’s 1/3 rules.

*UNIT IV* INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

Single step methods

Taylor’s series method

Euler’s method

Modified Euler’s method

Fourth order Runge

Kutta method for solving first order equations

Multi step methods

Milne’s and Adams

Bash forth predictor corrector methods for solving first order equations.

*UNIT V* BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS

Finite difference methods for solving second order two

Point linear boundary value problems

Finite difference techniques for the solution of two dimensional Laplace’s and Poisson’s equations on rectangular domain

One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods

One dimensional wave equation by explicit method.

**OUTCOMES**

Upon successful completion of the course, students should be able to:

- Understand the basic concepts and techniques of solving algebraic and transcendental

equations. - Appreciate the numerical techniques of interpolation and error approximations in various

intervals in real life situations. - Apply the numerical techniques of differentiation and integration for engineering problems.
- Understand the knowledge of various techniques and methods for solving first and second order ordinary differential equations.
- Solve the partial and ordinary differential equations with initial and boundary conditions by using certain techniques with engineering applications.

**TEXTBOOKS**

- Burden, R.L and Faires, J.D,
**“Numerical Analysis”**, 9th Edition, Cengage Learning, 2016. - Grewal, B.S., and Grewal, J.S.,
**“Numerical Methods in Engineering and Science”**, Khanna Publishers, 10th Edition, New Delhi, 2015.

**REFERENCES**

- Brian Bradie, “A Friendly Introduction to Numerical Analysis”, Pearson Education, Asia,

New Delhi, 2007. - Gerald. C. F. and Wheatley. P. O., “Applied Numerical Analysis”, Pearson Education, Asia, 6th Edition, New Delhi, 2006.
- Mathews, J.H. “Numerical Methods for Mathematics, Science and Engineering”, 2nd

Edition, Prentice Hall, 1992. - Sankara Rao. K., “Numerical Methods for Scientists and Engineers”, Prentice Hall of India Pvt. Ltd, 3rd Edition, New Delhi, 2007.
- Sastry, S.S, “Introductory Methods of Numerical Analysis”, PHI Learning Pvt. Ltd, 5th

Edition, 2015.