Uttarakhand Technical University 2009 B.Tech Mechanical Engineering Internal Mathematics rd - Question Paper

EAS-301/EAS-401: MATHEMATICS III

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Unit I : Function of Complex variable

Analytic function, C-R equations, Cauchys integral theorem, Cauchys integral formula for derivatives of

analytic function, Taylors and Laurents series, singularities, Residue theorem, Evaluation of real integrals of

the type and 10

Unit II : Statistical Techniques - I

Moments, Moment generating functions, Skewness, Kurtosis, Curve fitting, Method of least squares, Fitting of

straight lines, Polynomials, Exponential curves etc., Correlation, Linear, non linear and multiple regression

analysis, Probability theory. 08

Unit III : Statistical Techniques - II

Binomial, Poisson and Normal distributions, Sampling theory (small and large), Tests of significations: Chisquare

test, t-test, Analysis of variance (one way) , Application to engineering, medicine, agriculture etc.

Time series and forecasting (moving and semi-averages), Statistical quality control methods, Control charts, ,

R, p, np, and c charts. 08

Unit IV : Numerical Techniques I

Zeroes of transcendental and polynomial equation using Bisection method, Regula-falsi method and Newton-

Raphson method, Rate of convergence of above methods.

Interpolation: Finite differences, difference tables, Newtons forward and backward interpolation , Lagranges

and Newtons divided difference formula for unequal intervals. 08

Unit V : Numerical Techniques II

Solution of system of linear equations, Gauss- Seidal method, Crout method. Numerical differentiation,

Numerical integration , Trapezoidal , Simpsons one third and three-eight rules, Solution of ordinary

differential (first order, second order and simultaneous) equations by Eulers, Picards and forth-order Runge-

Kutta mehthods. 08

Test Books :-

1. Peter V. ONeil, Advance Engineering Mathematics Thomson (Cengage) Learning, 2007.

2. Jain, Iyenger & Jain, Numerical Methods for Scientific and Engineering Computation, New Age

International, New Delhi , 2003.

3. J.N. Kapur, Mathematical Statistics, S. Chand & company Ltd.,2000

Reference Books :-

1. R.K. Jain & S.R.K. Iyenger, Advance Engineering Mathematics, Narosa Publication House, 2002.

2. Chandrika Prasad, Advanced Mathematics for Engineers, Prasad Mudralaya, 1996.

3. E. Kreysig, Advanced Engineering Mathematics, John Wiley & Sons, 2005.

4. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 2005.

5. Devi Prasad, An introduction to Numerical Analysis, Narosa Publication house, New Delhi 2006.

6. T. Veerajan & T. Ramchandrandran, Theory & Problems in Numerical Methods, TMH, New Delhi,

2004.

7. S.P.Gupta, Statistical Methods, Sultan and Sons, New Delhi, 2004.

8. Devore, Probability and Statistics, Thomson(Cengage) Learning, 2007.

9. Walpole, Myers, Myers & Ye, Probability and Statistics for Engineers & Scientists, Pearson Education,

2003.