18MAT41 Complex Analysis, Probability and Statistical Methods syllabus for EC

Calculus of complex functions:

Review of function of a complex variable, limits, continuity, and differentiability. Analytic functions: Cauchy-Riemann equations in Cartesian and polar forms and consequences.

Construction of analytic functions:

Milne-Thomson method-Problems.

Conformal transformations:

Introduction. Discussion of transformations:
w=Z²  ,
w= e^z  , w
= z + 1/z ,(z ≠ 0).Bilinear transformations- Problems.

Complex integration:

Line integral of a complex function-Cauchy’s theorem and Cauchy’s integral formula and problems.

Probability Distributions:

Review of basic probability theory. Random variables (discrete and continuous), probability mass/density functions. Binomial, Poisson, exponential and normal distributions- problems (No derivation for mean and standard deviation)-Illustrative examples.

Statistical Methods:

Correlation and regression-Karl Pearson’s coefficient of correlation and rank correlation -problems. Regression analysis- lines of regression –problems. Curve Fitting: Curve fitting by the method of least squares- fitting the curves of the form- y = ax +b , y = ax^bandy = ax²+bx +c .

Joint probability distribution:

Joint Probability distribution for two discrete random variables, expectation and covariance.

Sampling Theory:

Introduction to sampling distributions, standard error, Type-I and Type-II errors. Test of hypothesis for means, student’s t-distribution, Chi-square distribution as a test of goodness of fit.

Course Outcomes:

At the end of the course the student will be able to:

• Use the concepts of analytic function and complex potentials to solve the problems arising in electromagnetic field theory.

• Utilize conformal transformation and complex integral arising in aerofoil theory, fluid flow visualization and image processing.

• Apply discrete and continuous probability distributions in analyzing the probability models arising in engineering field.

• Make use of the correlation and regression analysis to fit a suitable mathematical model for the statistical data.

• Construct joint probability distributions and demonstrate the validity of testing the hypothesis.

Question paper pattern:

• The question paper will have ten full questions carrying equal marks.

• Each full question will be for 20 marks.

• There will be two full questions (with a maximum of four sub- questions) from each module.

Textbooks

1 Advanced Engineering Mathematics E. Kreyszig John Wiley & Sons 10th Edition,2016

2 Higher Engineering Mathematics B. S. Grewal Khanna Publishers 44th Edition, 2017

3 Engineering Mathematics Srimanta Pal et al Oxford University Press 3 rd Edition,2016

Reference Books

1 Advanced Engineering Mathematics C. Ray Wylie, Louis C.Barrett McGraw-Hill 6 th Edition 1995

2 Introductory Methods of Numerical Analysis S.S.Sastry Prentice Hall of India 4 th Edition 2010

3 Higher Engineering Mathematics B. V. Ramana McGraw-Hill 11th Edition,2010

4 A Text Book of Engineering Mathematics N. P. Bali and Manish Goyal Laxmi Publications 2014

5 Advanced Engineering Mathematics Chandrika Prasad and Reena Garg Khanna Publishing, 2018

Web links and Video Lectures:

1. http://nptel.ac.in/courses.php?disciplineID=111

2. http://www.class-central.com/subject/math(MOOCs)

3. http://academicearth.org/

4. VTU EDUSAT PROGRAMME - 20