__MA3251__

__STATISTICS AND NUMERICAL METHODS__

**COURSE OBJECTIVES:**

•
This course aims at providing the necessary basic concepts of a few statistical
and numerical methods and give procedures for solving numerically different
kinds of problems occurring in engineering and technology.

•
To acquaint the knowledge of testing of hypothesis for small and large samples
which plays an important role in real life problems.

•
To introduce the basic concepts of solving algebraic and transcendental
equations.

•
To introduce the numerical techniques of interpolation in various intervals and
numerical techniques of differentiation and integration which plays an
important role in engineering and technology disciplines.

•
To acquaint the knowledge of various techniques and methods of solving ordinary
differential equations.

**UNIT I**

**TESTING OF HYPOTHESIS**

Sampling
distributions - Tests for single mean, proportion and difference of means
(Large and small samples) - Tests for single variance and equality of variances
- Chi square test for goodness of fit - Independence of attributes.

**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 differential
equations - Multi step methods: Milne's and Adams - Bash forth predictor
corrector methods for solving first order differential equations.

**TOTAL:
60 PERIODS**

** **

**COURSE 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:**

1.
Grewal, B.S., and Grewal, J.S., "Numerical Methods in Engineering and
Science", Khanna Publishers, 10th Edition, New Delhi, 2015.

2.
Johnson, R.A., Miller, I and Freund J., "Miller and Freund's Probability
and Statistics for Engineers", Pearson Education, Asia, 8th Edition, 2015.

**REFERENCES:**

1.
Burden, R.L and Faires, J.D, "Numerical Analysis", 9th Edition,
Cengage Learning, 2016.

2.
Devore. J.L., "Probability and Statistics for Engineering and the
Sciences", Cengage Learning, New Delhi, 8th Edition, 2014.

3.
Gerald. C.F. and Wheatley. P.O. "Applied Numerical Analysis" Pearson
Education, Asia, New Delhi, 7th Edition, 2007.

4.
Gupta S.C. and Kapoor V. K., "Fundamentals of Mathematical
Statistics", Sultan Chand & Sons, New Delhi, 12th Edition, 2020.

5.
Spiegel. M.R., Schiller. J. and Srinivasan. R.A., "Schaum's Outlines on
Probability and Statistics", Tata McGraw Hill Edition, 4th Edition, 2012.

6.
Walpole. R.E., Myers. R.H., Myers. S.L. and Ye. K., "Probability and
Statistics for Engineers and Probability and Statis Scientists", 9th
Edition, Pearson Education, Asia, 2010.