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UNIT-I
Functions of a Complex Variable and Complex Integration
Introduction – 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 – Generalized
Integral Formula (All Without Proofs) and Problems on Above Theorems.
UNIT-II
Series Expansions and Residue Theorem
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 f(x)dx
– 3
3#
and f(cos , sin ) d
c
c 2
q q q
+ r
#
UNIT-III
Probability and Distributions
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
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, χ2 and F-Distributions – Point and Interval Estimations – Maximum Error of Estimate.
UNIT-V
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.
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CategoriesEngineering
Format PDF
TypeeBook