# JNTUK B.TECH R20 2-2 Syllabus For Complex variables and statistical methods PDF 2022

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You will be able to find information about Complex variables 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 variables and statistical methods after reading this blog. Complex variables and statistical methods has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Complex variables 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 variables and statistical methods Unit One

#### Functions of a complex variable and Complex integration

Introduction – Continuity – Differentiability – Analyticity –Cauchy-Riemann equations in Cartesian and polar coordinates – Harmonicand conjugate harmonic functions – Milne – Thompson method.

Complex integration: Line integral – Cauchy’s integral theorem – Cauchy’s integral formula – Generalized integral formula (all without proofs) and problems on above theorems.

### Complex variables and statistical methods Unit Two

#### Series expansions and Residue Theorem

Radius of convergence – Expansion in Taylor’s series, Maclaurin’s series andLaurent series.

Types of Singularities: Isolated – Essential –Pole of order m– Residues – Residue theorem

(without proof) – Evaluation of real integral of the types

………………Column Break……………… f (x)dx and

………………Column Break………………c f (cos,sin )d .

### Complex variables and statistical methods Unit Three

#### Probability and Distributions

Review of probability and Baye’s theorem – Random variables – Discrete and Continuous random variables – Distribution functions – Probability mass function, Probability density function and Cumulative distribution functions – Mathematical Expectation and Variance – Binomial, Poisson, Uniform and Normal distributions

### Complex variables and statistical methods Unit Four

#### Sampling Theory

Introduction – Population and Samples – Sampling distribution of Means and Variance (definition only) – Central limit theorem (without proof) – Representation of the normal theory distributions –
Introduction to t, estimate.

………………Column Break……………… 2 and F-distributions – Point and Interval estimations – Maximum error of

### Complex variables and statistical methods Unit Five

#### Tests of Hypothesis

Introduction – Hypothesis – Null and Alternative Hypothesis – Type I and Type II errors – Level of significance – One tail and two-tail tests – Tests concerning one mean and two means (Large and Small samples) – Tests on proportions

### Complex variables and statistical methods Course Objectives

To familiarize the complex variables.

To make the student capable of evaluating the integrals in complex domains

To make the student capable of expanding a given function as a series and finding the poles and residues

To make the student capable of evaluating the integrals in complex domains using residue theorem

To familiarize the students with the foundations of probability and statistical methods.

To equip the students to solve application problems in their disciplines.

### Complex variables and statistical methods Course Outcomes

At the end of the course students will be able to

apply Cauchy-Riemann equations to complex functions in order to determine whether a given continuous function is analytic (L3)

find the differentiation and integration of complex functions used in engineering problems (L5)

make use of the Cauchy residue theorem to evaluate certain integrals (L3)

apply discrete and continuous probability distributions (L3)

design the components of a classical hypothesis test (L6)

infer the statistical inferential methods based on small and large sampling tests (L4)

### Complex variables and statistical methods Text Books

B. S. Grewal, Higher Engineering Mathematics, 44th Edition, Khanna Publishers.

Miller and Freund’s, Probability and Statistics for Engineers,7/e, Pearson, 2008

### Complex variables and statistical methods Reference Books

J. W. Brown and R. V. Churchill, Complex Variables and Applications, 9th edition, Mc- Graw Hill, 2013.

S.C. Gupta and V.K. Kapoor, Fundamentals of Mathematical Statistics, 11/e, Sultan Chand & Sons Publications, 2012.

Jay l. Devore, Probability and Statistics for Engineering and the Sciences, 8th Edition,Cengage.

Shron L.Myers, Keying Ye, Ronald E Walpole, Probability and Statistics Engineers and the Scientists,8th Edition, Pearson 2007.

Sheldon, M. Ross, Introduction to probability and statistics Engineers and the Scientists, 4thEdition, Academic Foundation,2011

### Scoring Marks in Complex variables and statistical methods

Information about JNTUK B.Tech R20 Complex variables and statistical methods was provided in detail in this article. To know more about the syllabus of other Engineering Subjects of JNTUH check out the official CynoHub application. Click below to download the CynoHub application.

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