MA6452 Statistics and Numerical Methods - Syllabus-Semester IV-MECH-BE-Anna University

NotesKhan MA6452 Statistics and Numerical Methods - Syllabus-Semester IV-MECH-BE-Anna University MECH SEM IV Syllabus, MECH SYLLABUS

 

 

 

MA6452                            STATISTICS  AND  NUMERICAL  METHODS                                L  T  P  C

3 1  0  4

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.

 

UNIT I             TESTING  OF HYPOTHESIS                                                                                    9+3

Large sample test based on Normal distribution for single mean and difference of means - Tests

 

based on t, c 2

 

and F distributions for testing means and variances – Contingency table (Test for

 

Independency) – Goodness of fit.

 

UNIT II            DESIGN OF  EXPERIMENTS                                                                                   9+3

One way and two way classifications - Completely randomized design – Randomized block design – Latin square design - 22   factorial design.

 

UNIT III           SOLUTION OF EQUATIONS  AND  EIGENVALUE  PROBLEMS                         9+3

Newton Raphson method – Gauss elimination method – pivoting – Gauss Jordan methods – Iterative methods of Gauss Jacobi and Gauss Seidel – Matrix inversion by Gauss Jordan method – Eigen values of a matrix by power method.

 

UNIT IV           INTERPOLATION, NUMERICAL DIFFERENTIATION AND NUMERICAL INTEGRATION                                                                                                           9+3

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         9+3

Taylor’s series method – Euler’s method – Modified Euler’s method – Fourth order Runge-Kutta method for solving first order equations – Milne’s predictor corrector methods for solving first order equations – Finite difference methods for solving second order equations.

TOTAL (L:45+T:15): 60 PERIODS

OUTCOMES

• It helps the students to have a clear perception of the power of statistical and numerical techniques, ideas and would be able to demonstrate the applications of these techniques to problems drawn from industry, management and other engineering fields.

 

TEXT BOOKS

1. Johnson. R.A., and Gupta. C.B., "Miller and Freund’s Probability and Statistics for  Engineers",

11th Edition, Pearson Education, , Asia, 2011.

2. Grewal. B.S., and Grewal. J.S., "Numerical Methods in Engineering and Science", 9th Edition, Khanna Publishers, New Delhi, 2007.

 

REFERENCES

1. 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.
2. Spiegel.  M.R.,  Schiller.  J.,  and  Srinivasan.  R.A.,  "Schaum’s  Outlines  on  Probability  and

Statistics", Tata McGraw Hill Edition, 2004.

3. Chapra. S.C., and Canale. R.P, "Numerical Methods for Engineers", 5th Edition, Tata McGraw

Hill, New Delhi, 2007.

4. Gerald. C.F., and Wheatley. P.O. "Applied Numerical Analysis" Pearson Education, Asia, New

Delhi, 2006.