# Mathematics - III

 Course Code : R13202 Author : uLektz University : JNTU Kakinada Regulation : 2016 Categories : General Engineering Format : ePUB3 (DRM Protected) Type : eBook

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Description :Mathematics - III of R13202 covers the latest syllabus prescribed by JNTU Kakinada for regulation 2016. 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 Linear systems of equations

1.1 Rank-Echelon form, Normal form

1.2 Solution of Linear Systems

1.3 Direct Methods- Gauss Elimination - Gauss Jordon and Gauss Seidal Methods

1.4 Application: Finding the current in a electrical circuit

###### UNIT II Eigen values - Eigen vectors and Quadratic forms

2.1 Eigen values - Eigen vectors – Properties

2.2 Cayley-Hamilton Theorem - Inverse and powers of a matrix by using Cayley-Hamilton theorem

2.4 Rank - Positive, negative definite - semi definite - index – signature

2.5 Application: Free vibration of a two-mass system

###### UNIT III Multiple integrals

3.1 Review concepts of Curve tracing (Cartesian - Polar and Parametric curves)

3.2 Applications of Integration to Lengths, Volumes and Surface areas of revolution in Cartesian and Polar Coordinates

3.3 Multiple integrals - double and triple integrals

3.4 Change of variables – Change of order of Integration

3.5 Application: Moments of inertia

###### UNIT IV Special functions

4.1 Beta and Gamma functions- Properties

4.2 Relation between Beta and Gamma functions

4.3 Evaluation of improper integrals

4.4 Application: Evaluation of integrals

###### UNIT V Vector Differentiation

5.2 Laplacian and second order operators

5.3 Vector identities

5.4 Application: Equation of continuity, potential surfaces

###### UNIT VI Vector Integration

6.1 Line integral -Work done

6.2 Potential function

6.3 Area - surface and volume integrals

6.4 Vector integral theorems: Greens, Stokes and Gauss Divergence Theorems (Without proof) and related problems

6.5 Application : work done, Force