**JNTUK R20-2 complex variables and statistical methods PDF Download**

Students taking JNTUK’s R20 Civil Branch, Can Download Unit-wise R20 2-2 Complex Statistics and Variables (CV&SM) Notes and Material Below are PDFs.

**OBJECTIVES:**

- To be familiar with the complicated variables.
- To make the student proficient in evaluating integrals of complex domains.
- to make the student capable of expanding a function into a series by locating the residues and poles
- To prepare the student for the task of evaluating integrals in complex domains with the help of residue theorem
- To help students understand the fundamentals of probability as well as techniques of statistical analysis.
- The students will be able to solve application problems within their respective disciplines.

**UNIT-1**

**The functions of complex variables complex integration**:

Introduction – Continuity & Differentiability – Analyticity â€“ Cauchy-Riemann formulas for Cartesian and polar coordinates Harmonic and conjugate harmonic function – Milne Thompson method. Thompson method. Complex integration: Line integral Cauchy’s integral theory – Cauchy’s basic formula – generalized essential formula (all without evidence) and other problems relating to the above theorems.

**UNIT-2**

**series expansions and Residue theorem:**Â the radius of convergence Expansion of Taylor’s series, Maclaurin’s Series, and Laurent series. The types of Singularities are: isolated the pole of order m Residues Essential The Residue Theorem ( with no proof) Assessment of the real integrals of the type fx DX

**UNIT-3**

**Probability and distributions**Â Review of Probability and Baye’s Theorem – Random variables – Continuous and Discrete variable random – distribution function – Probability mass function Probability density function Cumulative distribution functions Mathematical Expectation and Variance – Binomial Poisson Normal, Uniform, and normal distributions.

**UNIT-4:**

**Sampling Theory**Â Introduction – Samples and Populations The distribution of Sampling of Variance and Means (definition only) Central Limit Theorem (without proof) Representation of typical theory-based distributions Introductions to t 2, F and two distributions – Estimation of Intervals and Points – Maximum error of estimation.

**UNIT-5:**

**Tests of Hypothesis**Â An Introduction to Hypothesis â€“ Null and Alternative Hypothesis Type I as well as Type II mistakes The significance level – One-tail and two-tail tests – Tests involving one mean and two mean (Large and small samples) Tests of proportions.

**Textbooks:**

- 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.
- Sharon L. Myers, Keying Ye, Ronald E Walpole, Probability and Statistics Engineers, and the Scientists 8th Edition. Pearson 2007.
- Sheldon, M. Ross Sheldon, M. Ross, Introduction to Probability and statistical Engineers and the Scientists, 4th Edition, Academic Foundation, 2011

**OUTCOMES:**

- apply the Cauchy-Riemann equations on complex functions to determine if a continuous operation is analytical (L3)
- Find the integration and differentiation of complex functions used in engineering problems. (L5)
- Utilize to apply the Cauchy residue theorem to assess the properties of certain integrals (L3)
- Use continuous and discrete likelihood distributions (L3)
- Create the components of a traditional theory test (L6)
- use statistical inferential methods to determine the results using large and small testing of samples (L4)