Lecture Notes || SNS Courseware

Subject Details

Dept : EEE

Sem : 1

Regul : 2023

Faculty : Dr.S.Subhalakshmi

phone : 9095968068

E-mail : subha.s.math@snsct.org

371

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Lecture Notes

UNIT 1:

Determining Eigen values and Eigen vectors of a real matrix

Properties of Eigen values and Eigen vectors

Cayley Hamilton Theorem (statement only)-Problems

Cayley Hamilton Theorem –Applications

Eigen value problems arising from population models (Leslie model)

Determining Eigen values and Eigen vectors of a real matrix

UNIT 2:

Diagonalization of a real symmetric matrix

Quadratic form

Nature of the quadratic form

Applications: Stretching of an elastic membrane.

UNIT 3:

Radius of curvature in Cartesian Coordinates

Circle of Curvature in Cartesian Coordinates

Evolutes

Envelopes

UNIT 4:

Partial derivatives

Homogeneous functions and Euler’s theorem

Taylor’s series for functions of two variables

Lagrange’s Method of undetermined Multipliers

UNIT 5:

Double integration (Cartesian Coordinates)

Change of order of integration

Applications of double integral (Area)

Triple Integrals (Cartesian Coordinates)

Applications: Volume of solids

Lecture Notes