About Me

header ads

COMPLEX ANALYSIS, PROBABILITY AND STATISTICAL METHODS(18MAT41)

COMPLEX ANALYSIS, PROBABILITY AND STATISTICAL METHODS|azdocuments.in

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 special
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

Module-1

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.

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.

Click here to download Module-3

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


Module-5

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.

Click here to download Module-5


MODULE PAPER SOLUTIONS
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.

Click here to download complete handwritten notes

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.

Click here to download model question paper

Click here to download previous year question paper solutions


Textbook 

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 3rd 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 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=111
2. http://www.class-central.com/subject/math(MOOCs)
3. http://academicearth.org/
4. VTU EDUSAT PROGRAMME - 20


Softcopy Textbook Links:

1. ADVANCED ENGINEERING MATHEMATICS 10th ed ERWIN KREYSZIG Download Link


2. Higher Engineering Mathematics John Bird Download Link


3. CALCULUS EARLY TRANSCENDENTALS HOWARD ANTON & IRL BIVENS Download Link


4.  A Textbook of ENGINEERING MATHEMATICS-I  H.S. Gangwar Download Link

Hardcopy Textbook Links: