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Subject Details

Dept : IT

Sem : 1

Regul : 2019

Faculty : Mr. JAYARAM PRAKASH K

phone : NIL

E-mail : jayarammath@gmail.com

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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

TUTORIAL - 3

NATURE OF QUADRATIC FORM

UNIT 2:

SEQUENCES - DEFINITIONS AND EXAMPLES

SEQUENCE & SERIES , CONVERGENCE

TYPES OF CONVERGENCE

SERIES OF POSITIVE TERMS

TEST FOR CONVERGENCE - COMPARISON TEST

INTEGRAL TEST

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:

PARTIAL DERIVATIVE AND TOTAL DERIVATIVES

DIFFERENTIATION OF IMPLICIT FUNCTIONS, JACOBIAN AND PROPERTIES

PROBLEMS ON JACOBIAN

TAYLOR SERIES FOR FUNCTIONS OF TWO VARIABLES

MAXIMA AND MINIMA OF FUNCTIONS OF TWO VARIABLES

LAGRANGES METHOD

UNIT 5:

METHOD OF VARIATION OF PARAMETERS

HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS [P.I= x^n sinax(or) x^n cosax]

PROBLEMS ON METHOD OF VARIATION OF PARAMETERS

EULERS (CAUCHYS) LINEAR EQUATIONS

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