MA8452 Statistics and Numerical Methods Notes

MA8452 Statistics and Numerical Methods Notes
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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
22 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

  1. Grewal. B.S. and Grewal. J.S., “Numerical Methods in Engineering and Science ", 10th Edition, Khanna Publishers, 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, 2006.
  4. Spiegel. M.R., Schiller. J. and Srinivasan. R.A., "Schaum’s Outlines on Probability and Statistics ", Tata McGraw Hill Edition, 2004.
  5. 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.