JNTUK R20 B.Tech Mechanical 2-2 CVSM Material/ Notes PDF Download

JNTUK R20 B.Tech Mechanical 2-2 CVSM Material/ Notes PDF Download: The JNTUK R20 B.Tech Mechanical 2-2 CVSM Material helps students understand complex variables and statistical methods. It’s designed to teach the basics of these subjects and how they’re applied in different fields. This material is useful for solving real-world problems in their studies. Students can easily download the JNTUK R20 B.Tech Mechanical 2-2 CVSM Notes in PDF format to study effectively.

JNTUK R20 B.Tech Mechanical 2-2 CVSM Material – Units

Unit 1 Syllabus PDF Download | JNTUK R20 B.Tech Mechanical Complex Variables & Statistical Methods Material

Functions of a complex variable and Complex integration: Introduction – Continuity – Differentiability – Analyticity – Properties – 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).

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Unit 2 Syllabus PDF Download | JNTUK R20 B.Tech Mechanical Complex Variables & Statistical Methods Material

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 Syllabus PDF Download | JNTUK R20 B.Tech Mechanical Complex Variables & Statistical Methods Material

Probability and Distributions: Review of probability and Baye’s theorem – Random variables – Discrete and Continuous random variables – Distribution function – Mathematical Expectation and Variance – Binomial, Poisson, Uniform and Normal distributions.

Unit 4 Syllabus PDF Download | JNTUK R20 B.Tech Mechanical Complex Variables & Statistical Methods Material

Sampling Theory: Introduction – Population and samples – Sampling distribution of Means and Variance (definition only) – Central limit theorem (without proof) – Introduction to t, 2 and F-distributions – Point and Interval estimations – Maximum error of the estimate.

Unit 5 Syllabus PDF Download | JNTUK R20 B.Tech Mechanical Complex Variables & Statistical Methods Material

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.

JNTUK R20 B.Tech CVSM Material – Outcomes

• Use Cauchy-Riemann equations to check if a continuous function is analytic.
• Find derivatives and integrals of complex functions used in engineering problems.
• Evaluate certain integrals by applying the Cauchy residue theorem.
• Apply discrete and continuous probability distributions.
• Design classical hypothesis tests and make inferences based on statistical methods for small and large samples.

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