WITH EFFECT FROM THE ACADEMIC YEAR 2010 - 2011

MT 251

MATHEMATICS-IV

Instruction                                                                                              4 Periods per week

Duration of University Examination                                                      3 Hours

University Examination                                                                        75 Marks

Sessional                                                                                               25 Marks

UNIT-I: functions of Complex variables

Limit and Continuity of function – Analytic function- Cauchy – Reimann equations – complex integration, Cauchy’s theorem – Derivative of analytic functions – Cauchy’s integral formula and its applications.

UNIT-II: Taylor’s and Laurent’s Series Expansions

Zeroes and Singularities – Residues – Residue Theorem – Evaluation of real Integrals using Residue theorem – Conformal Mapping – Bilinear transformation.

UNIT-III:  Statistics

Random Variables, distributions, density functions – conditional distributions – Baye’s theorem – mathematical expectation, expected values – moments and Moment generating functions.

UNIT-IV:  Distributions

Poisson, Normal, Gamma and Chi-Square distribution – fitting curves to the data.

UNIT-V: Curve fitting by method of least squares

Correlation and Regression – lines of regression – Tests of Significance, Chi-Square, F and T-Tests.

Suggested Reading:

1. R.V. Churchill & J.W. Brown, Complex Variables and Applications, 5^th Edition, McGraw – Hill International Edition, 1990.
2. S.C. Gupta and V.K. Kapoor, Fundamentals of Mathematical Statistics, S. Chand & Co., New Delhi, 1997.
3. R.K. Jain & S.R.K. Iyengar, Advanced Engineering Mathematics, Narosa Publications, 2002.
4. B.V. Raman, Higher Engineering Mathematics, Core Engineering Series, Tata Mc Graw Hill Publishing Company Ltd., New Delhi, 2007.