Lecture Notes || SNS Courseware

Subject Details

Dept : AUTO

Sem : 1

Regul : 2019

Faculty : C.Saminathan

phone : NIL

E-mail : saminathan.c.math@snsct.org

352

Page views

Files

Videos

R.Links

Lecture Notes

UNIT 1:

Cayley Hamilton Theorem –Applications

Cayley Hamilton Theorem (statement only)-Problems

Properties of Eigen values and Eigen vectors

Eigen value problems arising from population models( Leslie model)

Determining Eigen values and Eigen vectors of a real matrix

UNIT 2:

Reduction of quadratic form to canonical form by orthogonal transformation

Nature of the quadratic form

Canonical form

Diagonalization of a real symmetric matrix

UNIT 3:

Curvature

Radius of curvature

Envelopes

Circle of Curvature

Evolutes

UNIT 4:

Partial derivatives

Jacobians

Taylor’s Expansion

Lagrange’s Method of undetermined Multipliers

UNIT 5:

Linear ODE with variable coefficients

Cauchy’s Linear differential equation

Legendre’s Linear differential equation

Method of Variation of parameters

Lecture Notes