Lecture Notes || SNS Courseware

Subject Details

Dept : IT

Sem : 1

Regul : 2023

Faculty : Ms. Prabha Sree

phone : 8754692928

E-mail : prabhasree.s.maths@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)

Determining Eigen values and Eigen vectors of a real matrix

UNIT 2:

Diagonalization of a real symmetric matrix

Quadratic form

Canonical form

Nature of the quadratic form

Applications: Stretching of an elastic membrane.

UNIT 3:

Curvature

Radius of curvature in Cartesian Coordinates

Circle of Curvature in Cartesian Coordinates

Evolutes

Centre of curvature

Envelopes

UNIT 4:

Homogeneous functions and Euler’s theorem

Partial derivatives

Lagrange’s Method of undetermined Multipliers

Lagrange’s of undetermined multipliers

Taylor’s series for functions of two variables

Applications: Maxima and minima of functions of two variables

UNIT 5:

Applications: Volume of solids

Applications of double integral(Area)

Change of order of integration

Applications: Maxima and minima of functions of two variables

Triple Integrals(Cartesian Coordinates)

Applications of double integral(Area)

Change of order of integration

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