Lecture Notes || SNS Courseware

Lecture Notes

UNIT 1:

1.1 INTRODUCTION TO MATRICES

1.2 Eigen Values And Eigen Vectors

1.3 Problems On Eigen Value And Eigen Vector

1.4 Tutorial 1

1.5 Properties

1.6 Cayley Hamilton Theorem

1.8 TUTORIAL

1.9 Reduction to Quadratic form

1.10 Problems on Reduction To Quadratic form

1.7 DIAGONALIZATION OF MATRICES

1.11 Nature of Quadratic form

1.12 TUTORIAL

UNIT 2:

2.1 SEQUENCES - DEFINITIONS AND EXAMPLES

2.2 SERIES - TYPES OF CONVERGENCE

2.3 SERIES OF POSITIVE TERMS

2.4 TEST FOR CONVERGENCE

2.5 INTEGRAL TEST

UNIT 3:

3.1 – CURVATURE AND RADIUS OF CURVATURE

3.2 – RADIUS OF CURVATURE

3.3 – CENTRE OF CURVATURE

3.4 – CIRCLE OF CURVATURE

3.5 – EVOLUTES

3.6 – EVOLUTES

3.7 – PROPERTIES OF EVOLUTES

3.8 – ENVELOPES

3.9 – ENVELOPES

UNIT 4:

4.1 PARTIAL DERIVATIVES AND TOTAL DERIVATIVES

4.2 JACOBIAN AND PROPERTIES

4.3- PROBLEMS ON JACOBIAN

4.4-TAYLOR SERIES FOR FUNCTIONS OF TWO VARIABLES

4.5-TAYLOR SERIES FOR FUNCTIONS OF TWO VARIABLES

4.6-MAXIMA AND MINIMA OF FUNCTIONS OF TWO VARIABLES

4.7-MAXIMA AND MINIMA OF FUNCTIONS OF TWO VARIABLES

4.6-MAXIMA AND MINIMA OF FUNCTIONS OF TWO VARIABLES

UNIT 5:

Differential equation variable coefficients

5.4-METHOD OF VARIATION OF PARAMETERS

5.5- Problems On Methods Of VariationOf Parameters

5.6 EULERS(CAUCHYS) LINEAR EQUATIONS