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Subject Details

Dept : MECH

Sem : 1

Regul : 2023

Faculty : R . MAREESWARI

phone : 7904785478

E-mail : mareeswari.r.math@snsce.ac.in

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Lecture Notes

UNIT 1:

Characteristic equations

Eigen values and Eigen vectors of a real matrix

TUTORIAL 1

Eigen values and Eigen vectors of a real matrix

Properties – Eigen values and Eigen vectors

Statement and applications of Cayley – Hamilton theorem

TUTORIAL 2

Diagonalization of Matrices

Reduction of quadratic form to canonical form by orthogonal transformation

Nature of quadratic form

TUTORIAL 3

UNIT 2:

Curvature in Cartesian coordinates

Centre and radius of curvature

Circle of curvature

Evolutes

Envelopes

TUTORIAL 4

TUTORIAL 5

TUTORIAL 6

UNIT 3:

Partial derivative and Total derivatives

Differentiation of implicit functions, Jacobian and properties

Problems on Jacobian

Maxima and minima of functions of two variables

Lagrange’s method

Lagrange’s method problems

UNIT 4:

Cauchys Linear equation

problems on method of variation of parameter

Homogeneous linear ODES Equations

UNIT 5:

Double integration (Cartesian co-ordinates)

Change of order of integration

Applications of double integral (Area)in cartesian coordinates

Triple Integration (Cartesian co-ordinates)

Volume as triple integrals and solids of revolution.

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