Lecture Notes || SNS Courseware

Subject Details

Dept : MECH

Sem : 1

Regul : 2019

Faculty : Ms.S.Gowsalyadevi

phone : NIL

E-mail : gowsimaths92@gmail.com

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Lecture Notes

UNIT 1:

Characteristic equations

Eigen values and Eigen vectors of a real matrix

Properties – Eigen values and Eigen vectors

Statement and applications of Cayley – Hamilton theorem

Reduction of quadratic form to canonical form by orthogonal transformation

Nature of quadratic form

Diagonalization of Matrices

UNIT 2:

Sequences: Definitions and examples.

Series: Types and convergence

Series of positive terms: Comparison test

Test of convergence-Comparison test

D’Alembert’s ratio test

UNIT 3:

Curvature in Cartesian coordinates

Centre and radius of curvature

Circle of curvature

Evolutes

Envelopes

Evolutes

UNIT 4:

Partial derivative and Total derivatives

Differentiation of implicit functions, Jacobian and properties

Problems on Jacobian

Taylor series for functions of two variables.

Maxima and minima of functions of two variables

Lagrange’s method

Lecture Notes