Lecture Notes || SNS Courseware

Subject Details

Dept : CSE

Sem : 1

Regul : 2023

Faculty : Poornavalli R

phone : 9042277564

E-mail : poorna.r.math@snsct.org

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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)

UNIT 2:

Diagonalization of a real symmetric matrix

Quadratic form

Nature of the quadratic form

Applications: Stretching of an elastic membrane.

Diagonalization of a real symmetric matrix

UNIT 3:

Radius of curvature in Cartesian Coordinates

Centre of curvature

Evolutes

Radius of curvature in Cartesian Coordinates

Envelopes

UNIT 4:

Partial derivatives

Homogeneous functions and Euler’s theorem

Taylor’s series for functions of two variables

Applications: Maxima and minima of functions of two variables

Lagrange’s Method of undetermined Multipliers

UNIT 5:

Change of order of integration

Double integration (Cartesian Coordinates)

Applications of double integral(Area)

Triple Integrals(Cartesian Coordinates)

Applications: Volume of solids

Lecture Notes