Subject Details
Dept     : CSE
Sem      : 1
Regul    : 2023
Faculty : P.M.Chellapandi
phone  : NIL
E-mail  : pmchellapandi1989@gmail.com
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Lecture Notes

UNIT 1:
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Eigen values and Eigen vectors of a real matrix
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Eigen values and Eigen vectors of a real matrix
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Eigen values and Eigen vectors of a real matrix
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Eigen values and Eigen vectors of a real matrix
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Properties of Eigen values and Eigen vectors
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Cayley Hamilton Theorem (statement only)-Problems
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Cayley Hamilton Theorem –Applications
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Eigen value problems arising from population models( Leslie model)
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Eigen value problems arising from population models( Leslie model)
UNIT 2:
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Diagonalization of a real symmetric matrix
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Diagonalization of a real symmetric matrix
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Quadratic form
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Canonical form
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Nature of the quadratic form
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Reduction of quadratic form to canonical form by orthogonal transformation
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Reduction of quadratic form to canonical form by orthogonal transformation
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Applications: Stretching of an elastic membrane.
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Applications: Stretching of an elastic membrane.
UNIT 3:
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Curvature
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Radius of curvature
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Centre of curvature
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Circle of Curvature
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Circle of Curvature
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Evolutes
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Evolutes
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Envelopes
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Envelopes
UNIT 4:
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Partial derivatives
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Partial derivatives
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Partial derivatives
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Homogeneous functions and Euler’s theorem
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Jacobians
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Taylor’s Expansion
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Applications: Maxima and minima of functions of two variables
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Lagrange’s Method of undetermined Multipliers
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Lagrange’s of undetermined Multipliers
UNIT 5:
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Double integration (Cartesian Coordinates)
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Double integration (Cartesian Coordinates)
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Change of order of integration
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Change of order of integration
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Change of order of integration
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Applications of double integral(Area)
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Applications of double integral(Area)
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Triple Integration(Cartesian Coordinates)
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Applications: Volume of solids