 # JNTUK B.TECH R20 2-1 Syllabus For Mathematics-iv PDF 2022

### Get Complete Lecture Notes for Mathematics-iv on Cynohub APP  You will be able to find information about Mathematics-iv 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 Mathematics-iv after reading this blog. Mathematics-iv has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Mathematics-iv 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.

All of the Topic and subtopics related to Mathematics-iv are mentioned below in detail. If you are having a hard time understanding Mathematics-iv or any other Engineering Subject of any semester or year then please watch the video lectures on the official CynoHub app as it has detailed explanations of each and every topic making your engineering experience easy and fun.

### Mathematics-iv Unit One

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

Introduction – Continuity – Differentiability – Analyticity –Cauchy-Riemann equations in Cartesian and polar coordinates – Harmonic and 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.

### Mathematics-iv Unit Two

#### Series expansions and Residue Theorem

Radius of convergence – Expansion in Taylor’s series, Maclaurin’s series and Laurent series. Types of Singularities: Isolated – Essential –Pole of order m– Residues – Residue theorem

### Get Complete Lecture Notes for Mathematics-iv on Cynohub APP  ### Mathematics-iv 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.

### Mathematics-iv 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, estimations – Maximum error of estimate.

………………Column Break……………… 2 and F-distributions – Point and Interval

### Mathematics-iv 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.

### Mathematics-iv Course Objectives

To familiarize the complex variables.

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

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

### Mathematics-iv 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)

### Mathematics-iv Text Books

B. S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 44th Edition, 2017.

Miller and Freund’s, Probability and Statistics for Engineers,Pearson,7th edition, 2008.

### Mathematics-iv 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, 11th edition, 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 Mathematics-iv  