# Complex Variables and Statistical Methods

Course Code:RT21024

Author:uLektz

University:

Regulation:2013

Categories:Electrical & Electronics

Format : ePUB3 (DRM Protected)

Type :eBook

Rs.199 Rs.30 Rs.85% off

Description :Complex Variables and Statistical Methods of RT21024 covers the latest syllabus prescribed by JNTU Kakinada for regulation 2013. Author: uLektz, Published by uLektz Learning Solutions Private Limited.

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

##### Topics
###### UNIT-I FUNCTIONS OF A COMPLEX VARIABLE

1.1 Introduction – Continuity – Differentiability-Analyticity – Properties

1.2 Cauchy-Riemann equations in Cartesian and polar coordinates

1.3 Harmonic and conjugate harmonic functions – Milne – Thompson method

###### UNIT-II INTEGRATION AND SERIES EXPANSIONS

2.1 Complex integration: Line integral – Cauchy’s integral theorem , Cauchy’s integral formula

2.2 Generalized integral formula (all without proofs) - Radius of convergence

2.3 Expansion in Taylor’s series, Maclaurin’s series and Laurent series

###### UNIT III INTEGRATION USING RESIDUES

3.1 Types of Singularities: Isolated, pole of order m, essential

3.2 Residues

3.3 Residue theorem( without proof)

3.4 Evaluation of real integrals of type (a) (b) (c)

###### UNIT IV CONFORMAL MAPPING

4.1 Transformation by exp z, lnz, z^2, z^n(n positive integer), Sin z, cos z, z + a/z-

4.2 Translation, rotation, inversion and bilinear transformation – fixed point – cross ratio – properties – invariance of circles.

###### UNIT V SAMPLING DISTRIBUTIONS

5.1 Review of Normal distribution - Population and samples

5.2 Sampling distribution of mean (with known and unknown variance)Proportion, variances

5.3 Sampling distribution of sums and differences -Point and interval estimators for means, variances, proportions

###### UNIT VI TESTS OF HYPOTHESIS

6.1 Type I and Type II errors

6.2 Maximum error- One tail, two-tail tests - Tests concerning one mean and proportion, two means

6.3 Proportions and their differences using Z-test, Student’s t-test - F-test and Chi -square test.