Subject Details
Dept     : CSE
Sem      : 1
Regul    : 2023
Faculty : S.YASODHA
phone  : 9500957774
E-mail  : yasodha.s.math@snsce.ac.in
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Lecture Notes

UNIT 1:
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Characteristic equations
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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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Statement and applications of Cayley – Hamilton theorem
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Diagonalization of matrices
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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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Nature of quadratic form
UNIT 2:
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Curvature in Cartesian coordinates
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Centre and radius of curvature
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Circle of curvature
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Evolutes
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Evolutes
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Envelope
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Envelope
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Centre and radius of curvature
UNIT 3:
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Partial derivative and Total derivatives
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Jacobian and properties
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Problems on Jacobian
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Maxima and minima of functions of two variables
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Maxima and minima of functions of two variables
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Lagrange’s method
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Problems on Lagrange’s method
UNIT 4:
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Eulers(Cauchys) linear equation
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Legendres linear equations
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Method of variation of parameters
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Problems on Method of variation of parameters