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__COMPLEX ANALYSIS, PROBABILITY AND STATISTICAL METHODS__

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Course Code:18MAT41
CIE Marks:40
SEE Marks:60
Teaching Hours/Week (L:T:P):(2:2:0)
Credits:03
Exam Hours:03

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Course Learning Objectives:

• To provide an insight into applications of complex variables, conformal mapping and specialCourse Learning Objectives:

functions 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.

__Scroll down to get complete handwritten notes and model question papers__

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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.

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__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.

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__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.

### Click here to download Module-3

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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-

### Click here to download Module-4

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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.

### Click here to download Module-5

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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.

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__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

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Reference Books

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

2 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

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Web links and Video Lectures:

1. http://nptel.ac.in/courses.php?disciplineID=111Web links and Video Lectures:

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

3. http://academicearth.org/

4. VTU EDUSAT PROGRAMME - 20

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