Looking for the latest JNTU-CVSM Subject Material 2024? Stay updated with our comprehensive guide on all the important topics and resources you need to excel in your studies. CVSM : Complex Variables and Statistical Methods
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UNIT – I: Functions of a complex variable and Complex integration: (10 hrs)
Introduction – Continuity – Differentiability – Analyticity –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) and problems on above theorems.
UNIT – II: Series expansions and Residue Theorem: (10 hrs)
Radius of convergence – Expansion in Taylor’s series, Maclaurin’s series and Laurent series.
Types of Singularities: Isolated – Essential –Pole of order m– Residues – Residue theorem
(without proof) – Evaluation of real integral of the types
UNIT – III: Probability and Distributions: (10 hrs)
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 – IV: Sampling Theory: (8 hrs)
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, and F-distributions – Point and Interval
estimations – Maximum error of estimate.
UNIT – V: Tests of Hypothesis: (10 hrs)
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.