**JNTUK R20 2-2 Complex Variables and Statistical Methods Material PDF Download**

Students those who are studying JNTUK R20 Civil Branch, Can Download Unit wise R20 2-2 Complex Variables and Statistical Methods (CV&SM) Material/Notes PDFs below.

### JNTUK R20 2-2 Complex Variables and Statistical Methods Material PDF Download

**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.

**UNIT-1**

**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.

**UNIT-2**

**Series expansions and Residue Theorem:** Radius of convergence – Expansion in Taylor’s series, Maclaurin’s series and Laurent series. Types of Singularities: Isolated – pole of order m – Essential – Residues – Residue theorem ( without proof) – Evaluation of real integral of the type f x dx

**UNIT-3 **

**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.

**UNIT-4: **

**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, 2 and F-distributions – Point and Interval estimations – Maximum error of estimate.

**UNIT-5: **

**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.

**TEXT BOOKS: **

- B. S. Grewal, Higher Engineering Mathematics, 43rd Edition, Khanna Publishers.
- Miller and Freund’s, Probability and Statistics for Engineers, 7/e, Pearson, 2008.

**REFERENCES: **

- J. W. Brown and R. V. Churchill, Complex Variables and Applications, 9th edition, McGraw 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, 4th Edition, Academic Foundation, 2011

**OUTCOMES:**

- 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)