Lecture Notes || SNS Courseware

Subject Details

Dept : EEE

Sem : 1

Regul : 2019

Faculty : S.Sindhuja

phone : NIL

E-mail : sindhuja.171@gmail.com

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Lecture Notes

UNIT 1:

Determining Eigen values and Eigen vectors of a real matrix

Properties of Eigen values and Eigen vectors

Cayley Hamilton Theorem (statement only)-Problems

Cayley Hamilton Theorem –Applications

UNIT 2:

Diagonalization of a real symmetric matrix

Quadratic form

Canonical form

Nature of the quadratic form

Reduction of quadratic form to canonical form by orthogonal transformation

UNIT 3:

Curvature

Radius of curvature

Centre of curvature

Circle of Curvature

Evolutes

Envelopes

UNIT 4:

Partial derivatives

Total derivatives

Jacobians

Taylor’s Expansion

Maxima and Minima

Lagrange’s Method of undetermined Multipliers

UNIT 5:

Linear ODE with variable coefficients

Homogeneous Linear ODE’s with constant coefficients

Cauchy’s Linear differential equation

Legendre’s Linear differential equation

Method of Variation of parameters

Lecture Notes