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= ez , 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 = axbandy = 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