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Subject Details

Dept : MCT

Sem : 1

Regul : 2019

Faculty : Ms B Abarna

phone : NIL

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

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Lecture Notes

UNIT 1:

INTRODUCTION TO MATRICES

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:

SEQUENCES - DEFINITIONS AND EXAMPLES

SEQUENCE & SERIES , CONVERGENCE

TYPES OF CONVERGENCE

SERIES OF POSITIVE TERMS

TEST FOR CONVERGENCE - COMPARISON TEST

INTEGRAL TEST

ABSOLUTE AND CONDITIONAL CONVERGENCE

UNIT 3:

CURVATURE AND RADIUS OF CURVATURE

RADIUS OF CURVATURE

CENTRE OF CURVATURE

CIRCLE OF CURVATURE

EVOLUTES

PROBLEMS ON EVOLUTES

PROPERTIES OF EVOLUTES

ENVELOPES

PROBLEMS ON ENVELOPES

UNIT 4:

Introduction to partial derivative and total derivative

Jacobian and properties

Problems on Jacobian

Tutorial 10

Taylors series

Problems on Taylors series

Maxima and minima

Tutorial 11

Problems on Maxima and minima

Tutorial 12

UNIT 5:

Higher order linear ODE with constant coefficient

Cauchy linear equation

Method of variation of parameter

Tutorial

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