JNTUK R20 2-2 Complex Variables and Statistical Methods Material | Full Notes PDF Download

JNTUK R20-2 complex variables and statistical methods PDF Download

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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.


  • 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.


The functions of complex variables complex integration:

Introduction – Continuity & Differentiability – Analyticity – 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-1 PDF Material Download


series expansions and Residue theorem: 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-2 Materials PDF Download


Probability and distributions 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-3 PDF Material Download


Sampling Theory 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-4 Materials PDF Download


Tests of Hypothesis An Introduction to Hypothesis – 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.

Unit-5 Materials PDF Download



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


  1. J. W. Brown and R. V. Churchill, Complex Variables and Applications 9th edition McGraw Hill, 2013
  2. S. C. Gupta and V. K. Kapoor, Fundamentals of Mathematical Statistics 11/e Sultan Chand & Sons Publications 2012.
  3. Jay l. Devore, Probability, and Statistics for Engineering and the Sciences 8th Edition Cengage.
  4. Sharon L. Myers, Keying Ye, Ronald E Walpole, Probability and Statistics Engineers, and the Scientists 8th Edition. Pearson 2007.
  5. Sheldon, M. Ross Sheldon, M. Ross, Introduction to Probability and statistical Engineers and the Scientists, 4th Edition, Academic Foundation, 2011


  • 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)

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