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Subject Details

Dept : MECH

Sem : 1

Regul : 2023

Faculty : Gomathi P

phone : NIL

E-mail : gomathisenthilkumar2011@gmail.com

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Lecture Notes

UNIT 1:

Eigen values and Eigen vectors of a real matrix

Cayley Hamilton Theorem (statement only)-Problems

Cayley Hamilton Theorem â€“Applications

Properties of Eigen values and Eigen vectors

Eigen value problems arising from population models( Leslie model)

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

Applications: Stretching of an elastic membrane.

UNIT 3:

Curvature

Radius of curvature

Centre of curvature

Circle of Curvature

Envelopes

Evolutes

Envelopes

UNIT 4:

Partial derivatives

Homogeneous functions and Eulerâ€™s theorem

Jacobians

Taylorâ€™s Expansion

Applications: Maxima and minima of functions of two variables

Lagrangeâ€™s Method of undetermined Multipliers

UNIT 5:

Double integration (Cartesian Coordinates)

Change of order of integration

Applications of double integral(Area)

Triple Integration(Cartesian Coordinates)

Applications: Volume of solids

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