Subject Details
Dept     : CSE
Sem      : 1
Regul    : 2023
Faculty : R . MAREESWARI
phone  : 7904785478
E-mail  : mareeswari.r.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 – 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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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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Envelopes
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Envelopes
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Envelopes
UNIT 3:
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Partial derivative and Total derivatives
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Problems on Jacobian
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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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Lagrange’s method
UNIT 4:
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Higher order linear differential equations with constant coefficients (RHS = eax, sinax(or) cosax)
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Method of variation of parameters
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Eulers(Cauchys) linear equations
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Eulers(Cauchys) linear equations
UNIT 5:
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Applications of double integral (Area)in cartesian coordinates
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Change of order of integration problems
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Double integration (Cartesian co-ordinates)
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Triple Integration
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Volume as triple integrals and solids of revolution.