# Mathematics- II

 Course Code : BMA201 Author : Ulektz University : Bharath University, Tamil Nadu (BU) Regulation : 2015 Categories : Engineering Mathematics Format : ePUB3 (DRM Protected) Type : eBook

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Description :Mathematics- II of BMA201 covers the latest syllabus prescribed by Bharath University, Tamil Nadu (BU) for regulation 2015. 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 Ordinary Differential Equation

1.1 Higher order linear differential equations with constant coefficients

1.2 Method of variation of parameters

1.3 Cauchy’s and Legendre’s linear equations

1.4 Simultaneous first order linear equations with constant coefficients\

###### UNIT II Vector Calculus

2.1 Gradient,divergence and curl - Directional derivatives - Irrotational and solenoidal vector fields

2.2 Vector integration

2.3 Green’s theorem in a plane

2.4 Gauss divergence theorem

2.5 Stoke’s theorem (without proofs)

2.6 Simple applications involving cubes and rectangular parallelepipeds

###### UNIT III Analytic Functions

3.1 Functions of a complex variable

3.2 Analytic functions - Necessary conditions

3.3 Cauchy-Riemann equation and sufficient conditions (without proofs)

3.4 Harmonic and orthogonal properties of analytic functions

3.5 Harmonic conjugate

3.6 Construction of analytic functions

3.7 Conformal mapping : W= Z+C,CZ , 1/Z - Bilinear transformation

###### UNIT IV Complex Integration

4.1 Complex integration

4.2 Statement and application of Cauchy’s integral theorem and Cauchy’s integral formula

4.3 Taylor and Laurent expansions

4.4 Singular points

4.5 Residues

4.6 Residue theorem

4.7 Application of Residue theorem to evaluate real integrals - Unit circle and semi-circular contour (excluding ploes on boundaries)

###### UNIT V Statistics

5.1 Mean, Median,Mode

5.2 Moments

5.3 Skewness and Kurtosis

5.4 Correlation - Rank Correlation - Regression

5.5 Chi square test for contingency tables