COMPLEX ANALYSIS, PROBABILITY AND STATISTICAL METHODS
Course Code:18MAT41
CIE Marks:40
SEE Marks:60
Teaching Hours/Week (L:T:P):(2:2:0)
Credits:03
Exam Hours:03
Course Learning Objectives:
• To provide an insight into applications of complex variables, conformal mapping and specialfunctions arising in potential theory, quantum mechanics, heat conduction and field theory.
• To develop probability distribution of discrete, continuous random variables and joint
probability distribution occurring in digital signal processing, design engineering and
microwave engineering.
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Module-1
Calculus of complex functions: Review of function of a complex variable, limits, continuity, anddifferentiability. Analytic functions: Cauchy-Riemann equations in Cartesian and polar forms and
consequences.
Construction of analytic functions: Milne-Thomson method-Problems.
Module-2
Conformal transformations: Introduction. Discussion of transformations: Bilinear transformations- Problems.Complex integration: Line integral of a complex function-Cauchy’s theorem and Cauchy’s integral formula
and problems.
Module-3
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.
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Module-4
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-
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Module-5
Joint probability distribution: Joint Probability distribution for two discrete random variables, expectationand 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.
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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:
5. The question paper will have ten full questions carrying equal marks.6. Each full question will be for 20 marks.
• There will be two full questions (with a maximum of four sub-questions) from each module.
Textbook
1 Advanced Engineering Mathematics E. Kreyszig John Wiley & Sons 10th Edition,20162 Higher Engineering Mathematics B. S. Grewal Khanna Publishers 44th Edition, 2017
3 Engineering Mathematics Srimanta Pal et al Oxford University Press 3rd Edition,2016
Reference Books
1 Advanced Engineering Mathematics C. Ray Wylie, Louis C.Barrett McGraw-Hill 6 th Edition 19952 Introductory Methods of Numerical Analysis S.S.Sastry Prentice Hall of India 4th 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
Web links and Video Lectures:
1. http://nptel.ac.in/courses.php?disciplineID=1112. http://www.class-central.com/subject/math(MOOCs)
3. http://academicearth.org/
4. VTU EDUSAT PROGRAMME - 20
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