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Subject Details

Dept : ECE

Sem : 1

Regul : 2019

Faculty : Mr B.Mohan

phone : Nil

E-mail : mohan.b.math@snsce.ac.in

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Lecture Notes

UNIT 1:

Eigen values and Eigenvectors of real matrix

EIGEN VALUES AND EIGEN VECTORS

PROBLEMS ON EIGEN VALUES AND EIGEN VECTORS

TUTORIAL - 1

PROPERTIES OF EIGEN VALUES AND EIGEN VECTORS

CAYLEY HAMILTON THEOREM

DIAGONALIZATION OF MATRICES

TUTORIAL - 2

REDUCTION OF QUADRATIC FORM TO CANONICAL FORM

PROBLEMS ON REDUCTION OF QUADRATIC FORM

NATURE OF QUADRATIC FORM

TUTORIAL - 3

UNIT 2:

2.1 INTRODUCTION SEQUENCE AND SERIES

TYPES AND CONVERGENCE SERIES OF POSITIVE TERMS

TEST OFCONVERGENCE

COMPARISON TEST

INTEGRAL TEST

ALTERNATIVE SERIES - LEBNITZ TEST

ABSOLUTE TEST

TUTORIAL - 6

UNIT 3:

DEFINE - CURVATURE

CURVATURE INCARTESIAN COORDINATES

CENTRE AND CURVATURE

CIRCLE OF CURVATURE

PROBLEMS ON CIRCLE OF CURVATURE

EVOLUTES

PROBLEMS ON EVOLUTES

ENVELOPS

PROBLEMS ON ENVELOPS

UNIT 4:

JACOBIAN AND PROPERTIES

Introduction of partial derivative

PROBLEMS ON JACOBIAN

TUTORIAL - 10

TAYLOR SERIES

TAYLOR SERIES PROBLEMS

MAXIMA AND MINIMA

LEGRANGES METHOD

PROBLEMS ON LEGRANGES METHOD

UNIT 5:

higher order linear differential equation with constant coefficient

Cauchy’s linear equation

Method of variation of parameters

Problems ofLegendre’s Equations

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