# MMC105

## NUMERICAL AND STATISTICAL METHODS

OBJECTIVE : To develop computing and program writing skills.

PREREQUISITE : Ancillary Mathematics at degree level

1. INTRODUCTION AND ALGEBRAIC EQUATIONS 
Errors in Numerical approximations: Sources and various types of errors — Chopping and Rounding in different numbers systems — Stability of Numerical algorithms.
Transcendental and polynomial equation: Iterative method, Regular-Falsi Method, Newton Raphson method, Roots of polynomials — Graeffe’s and Bairstow methods.

2. SYSTEM OF EQUATIONS AND INTERPOLATION 
Solution of system of linear algebraic equations: Gauss Elimination, Gauss Jordan method, Jacobi and Gauss — Seidal methods. Interpolation — Polynomial interpolation, Lagrange and Newton interpolation, Piecewise polynomial interpolation, Cubic splines, Data fitting, Method of least squares.

3. DIFFERENTIAL EQUATIONS 
Euler’s method and its modified form, Range Kutta method of fourth order, Predictor, Corrector methods, Miline’s method, Adams—Moulton method.

4. PROBABILITY DISTRIBUTION AND CORRELATION 
Binomial, Poisson and Normal Distribution — Fitting of probability distributions — Correlation and regression, Linear regression, Correlation coefficient, Multiple linear regression.

5. TESTS OF HYPOTHESIS 
Tests of Hypothesis — Testing for Attributes — Mean of Normal Population — One- tailed and Two- tailed tests — Student T-test, F-test — Chi-Square test — ANOVA — One way and Two way Classifications.

TEXT BOOKS:
1. M.K.Jain et al, “Numerical Methods for Scientific & Engg. Computation”, 1995, Wisely Eastern Limited.
2. G.W. Snedcor, W.G. Cochrass,”Statistical Methods”, 6 Edn, East West Press.
3. S.C. Gupta, “Introduction to Mathematical Statistics”, 1973, Sultan Chand.
4. S.C. Chapra and R.P. Canale “Numerical Methods for Engineers”, 2002, Tata McGraw Hill.

REFERENCES:
1. J. Thomas King,” Introduction to Numerical Computation”, 1988, McGraw Hill.
2. John, R.Rice, “Numerical Methods: Software and Analysis”, 1983, McGraw Hill.
3. David Kahn et al, “Numerical Methods and Software”, 1989, PHI.