Regulation: R23 Branch: Mechanical Engineering Semester: 2-2 Code: 23FE13

Complex Variables, Probability and Statistics

Verified vs. official syllabus Checked 2026-07-01

Both the subject list and detailed unit topics are sourced from an autonomous JNTUK-affiliated college's published syllabus and have not been independently cross-confirmed against JNTUK's own exam records -- autonomous colleges may adapt content locally.

Unit-wise syllabus

UNIT 01

Complex Variables & Complex Integration

Continuity, differentiability, analyticity; Cauchy-Riemann equations in Cartesian and polar coordinates; Harmonic and conjugate harmonic functions; Milne-Thomson method; Complex integration: line integral, Cauchy's integral theorem; Cauchy's integral formula and generalized integral formula (without proofs)

UNIT 02

Series Expansions & Residue Theorem

Radius of convergence; Taylor's, Maclaurin's and Laurent series; Types of singularities: isolated, essential and pole of order m; Residues and residue theorem (without proof); Evaluation of real integrals using the residue theorem

UNIT 03

Probability and Distributions

Review of probability and Baye's theorem; 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 04

Sampling Theory

Population and samples; sampling distribution of means and variance; Central limit theorem (without proof); representation of normal theory distributions; Introduction to t, chi-square and F distributions; Point and interval estimations; maximum error of estimate

UNIT 05

Tests of Hypothesis

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