Lecture Notes

Dear Students the Lecture Notes has been uploaded for the following topics:
Characteristic equations ,
Eigen values and Eigen vectors of a real matrix,
Properties – Eigen values and Eigen vectors,
Statement and applications of Cayley – Hamilton theorem ,
Diagonalization of Matrices,
Reduction of quadratic form to canonical form by orthogonal transformation,
Nature of quadratic form,
Curvature in Cartesian coordinates,
Centre and radius of curvature,
Circle of curvature,
Evolutes,
Envelopes,
Partial derivative and Total derivatives ,
Problems on Jacobian ,
Maxima and minima of functions of two variables,
Lagrange’s method,
Higher order linear differential equations with constant coefficients (RHS = eax, sinax(or) cosax),
Method of variation of parameters,
Eulers(Cauchys) linear equations,
Applications of double integral (Area)in cartesian coordinates,
Change of order of integration problems,
Double integration (Cartesian co-ordinates) ,
Triple Integration ,
Volume as triple integrals and solids of revolution.