# MATHEMATICS-III

 Course Code : 13A54302 Author : uLektz University : Jawaharlal Nehru Technological University, Anantapur (JNTUA) Regulation : 2013 Categories : Electronics & Communication Format : ePUB3 (DRM Protected) Type : eBook

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Description :MATHEMATICS-III of 13A54302 covers the latest syllabus prescribed by Jawaharlal Nehru Technological University, Anantapur (JNTUA) 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:Special Functions

1.1 Gamma and Beta Functions Their Properties

1.2 Evaluation of improper integrals

1.3 Series Solutions of ordinary differential equations (Power series and Frobenius Method).

###### Unit II:Bessel functions

2.1 Properties ,Recurrence relations,Orthogonality

2.2 Legendre polynomials,Properties, Rodrigue’s formula,Recurrence relations

###### Unit III:Functions of a complex variable

3.1 Continuity Differentiability,Analyticity – Properties,Cauchy-Riemann equations in Cartesian and polar coordinates

3.2 Harmonic and conjugate harmonic functions,Milne Thompson method

3.3 Conformal mapping: Transformation of ez, Inz, z2, Sinz, cosz, Bilinear transformation, Translation, rotation, magnification and inversion

3.4 Fixed point, Cross ratio, Determination of bilinear transformation

###### Unit IV: Complex integration

4.1 Line integral Evaluation along a path and by indefinite integration,Cauchy’s integral theorem,Cauchy’s integral formula,Generalized integral formula

4.2 Complex power series: Radius of convergence,Expansion in Taylor’s series Maclaurin’s series and Laurent series

4.3 Isolated singular point,Pole of order m,Essential singularity

###### Unit V:Residue

5.1 Evaluation of residue by formula and by Laurent series,Residue theorem

5.2 Evaluation of integrals of the type (a) improper real integrals