*UNIT I* TESTING OF HYPOTHESIS

Sampling distributions

Estimation of parameters

Statistical hypothesis

Large sample tests based on Normal distribution for single mean and difference of means

Tests based on t,

Chi-square and F distributions for mean,

variance and proportion

Contingency table (test for independent)

Goodness of fit.

*UNIT II* DESIGN OF EXPERIMENTS

One way and two way classifications

Completely randomized design

Randomized block design

Latin square design

2^{2} factorial design.

*UNIT III* 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 IV* INTERPOLATION, NUMERICAL DIFFERENTIATION AND NUMERICAL

**INTEGRATION**

Lagrange’s and Newton’s divided difference interpolations

Newton’s forward and backward difference interpolation

Approximation of derivates using interpolation polynomials

Numerical single and double integrations using Trapezoidal and Simpson’s 1/3 rules.

*UNIT V* NUMERICAL SOLUTION OF 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.

**OUTCOMES**

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

- Apply the concept of testing of hypothesis for small and large samples in real life problems.
- Apply the basic concepts of classifications of design of experiments in the field of agriculture.
- Appreciate the numerical techniques of interpolation in various intervals and 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.

**TEXT BOOKS**

- Grewal. B.S. and Grewal. J.S.,
**“Numerical Methods in Engineering and Science "**, 10th Edition, Khanna Publishers, New Delhi, 2015. - Johnson, R.A., Miller, I and Freund J.,
**“Miller and Freund’s Probability and Statistics for****Engineers"**, Pearson Education, Asia, 8th Edition, 2015.

**REFERENCES**

- Burden, R.L and Faires, J.D, "Numerical Analysis”, 9th Edition, Cengage Learning, 2016.
- Devore. J.L., "Probability and Statistics for Engineering and the Sciences”, Cengage Learning, New Delhi, 8th Edition, 2014.
- Gerald. C.F. and Wheatley. P.O. "Applied Numerical Analysis” Pearson Education, Asia, New Delhi, 2006.
- Spiegel. M.R., Schiller. J. and Srinivasan. R.A., "Schaum’s Outlines on Probability and Statistics ", Tata McGraw Hill Edition, 2004.
- Walpole. R.E., Myers. R.H., Myers. S.L. and Ye. K., “Probability and Statistics for Engineers and Scientists", 8th Edition, Pearson Education, Asia, 2007.