Lecture Notes || SNS Courseware

Subject Details

Dept : MCT

Sem : 1

Regul : 2023

Faculty : S.YASODHA

phone : 9500957774

E-mail : yasodha.s.math@snsce.ac.in

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Lecture Notes

UNIT 1:

1 Characteristic equations

Eigen values and Eigen vectors of a real matrix

Statement and applications of Cayley – Hamilton theorem

Properties – Eigen values and Eigen vectors

Reduction of quadratic form to canonical form by orthogonal transformation

Nature of quadratic form

UNIT 2:

Curvature in Cartesian coordinates

Centre and radius of curvature

Circle of curvature

Evolutes

Envelopes

UNIT 3:

Partial derivative and Total derivatives

Jacobian and properties

Problems on Jacobian

Maxima and minima of functions of two variables

Problems on Maxima and minima of functions of two variables

Lagrange’s method

UNIT 4:

Eulers(Cauchys) linear equations

Method of variation of parameters

Legendres linear equations

Lecture Notes