Book Details

Mathematics

Mathematics

Published by uLektz

Course Code : ULZHS0054
Author : uLektz
University : General for All University
Regulation : 2013
Categories : Arts and Science
Format : ico_bookePUB3 (DRM Protected)
Type : eBook

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Description :Mathematics of ULZHS0054 covers the latest syllabus prescribed by General for All University 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 LINEAR SYSTEMS OF EQUATIONS

1.1 Rank-Echelon form-Normal form

1.2 Solution of linear systems

1.3 Gauss elimination,Gauss Jordon

1.4 Gauss Jacobi and Gauss Seidal methods

1.5 Applications: Finding the current in electrical circuits

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

2.3 Diagonalization

2.4 Quadratic forms- Reduction of quadratic form to canonical form

2.5 Rank-Positive, negative and semi definite-Index-Signature

2.6 Applications: Free vibration of a two-mass system

UNIT - III MULTIPLE INTEGRALS

3.1 Curve tracing: Cartesian, Polar and Parametric forms

3.2 Multiple integrals: Double and triple integrals

3.3 Change of variables

3.4 Change of order of integration

3.5 Applications: Finding Areas and Volumes

UNIT - IV SPECIAL FUNCTIONS

4.1 Beta and Gamma functions-Properties

4.2 Relation between beta and gamma functions and simple problems

4.3 Evaluation of improper integrals

4.4 Application: Evaluation of integrals

UNIT - V VECTOR DIFFERENTIATION

5.1 Gradient, Divergence, Curl

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,Green’s theorem,Stoke’s theorem,Gauss's Divergence Theorem

6.5 Application: Work done, Force

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