 # VTU B.TECH AERONATICAL-Engineering 3rd SEM Syllabus For Complex analysis, probability and statistical methods PDF 2022

### Get Complete Lecture Notes for Complex analysis, probability and statistical methods on Cynohub APP  You will be able to find information about Complex analysis, probability and statistical methods along with its Course Objectives and Course outcomes and also a list of textbook and reference books in this blog.You will get to learn a lot of new stuff and resolve a lot of questions you may have regarding Complex analysis, probability and statistical methods after reading this blog. Complex analysis, probability and statistical methods has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Complex analysis, probability and statistical methods can be learnt easily as long as you have a well planned study schedule and practice all the previous question papers, which are also available on the CynoHub app.

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### Complex analysis, probability and statistical methods Unit One

#### 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.

### Complex analysis, probability and statistical methods Unit Two

#### Module-2

Conformal transformations: Introduction. Discussion of transformations:ᡵ=ᡒ⡰,ᡵ=ᡗこ,ᡵ=ᡸ+⡩こ,䙦ᡸ≠0䙧.Bilinear transformations- Problems.Complex integration: Line integral of a complex function-Cauchy’s theorem and Cauchy’s integral formula and problems.

### Get Complete Lecture Notes for Complex analysis, probability and statistical methods on Cynohub APP  ### Complex analysis, probability and statistical methods Unit Three

#### 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.

### Complex analysis, probability and statistical methods Unit Four

#### 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-ᡷ=ᡓᡶ+ᡔ,ᡷ=ᡓᡶ〩ᡓᡦᡖᡷ=ᡓᡶ⡰+ᡔᡶ+ᡕ.

### Complex analysis, probability and statistical methods Unit Five

#### 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.

### Complex analysis, probability and statistical methods Course 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.

### Complex analysis, probability and statistical methods 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 inengineering 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.

### Complex analysis, probability and statistical methods Text Books

Higher Engineering Mathematics-B. S. Grewal
Engineering Mathematics-Srimanta Pal et al

### Complex analysis, probability and statistical methods Reference Books

Advanced Engineering Mathematics-C. Ray Wylie, Louis C.Barrett
Introductory Methods of Numerical Analysis-S.S.Sastry
Higher Engineering Mathematics-B. V. Ramana
A Text Book of Engineering Mathematics-N. P. Bali and Manish Goyal

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