Eigenvalues and Eigenvectors of a real matrix Characteristic equation Properties of eigenvalues and eigenvectors Statement and applications of Cayley-Hamilton Theorem Diagonalization of matrices Reduction of a quadratic form to canonical form by orthogonal transformation Nature of quadratic forms.
Curvature in Cartesian co-ordinates Centre and radius of curvature Circle of curvature Evolutes Envelopes - Evolute as envelope of normals.
Curvature in Cartesian co-ordinates Centre and radius of curvature Circle of curvature Evolutes Envelopes - Evolute as envelope of normals.
Limits and Continuity Partial derivatives Total derivative Differentiation of implicit functions Jacobian and properties Taylors series for functions of two variables Maxima and minima of functions of two variables Lagranges method of undetermined multipliers.
Double integrals in cartesian and polar coordinates Change of order of integration Area enclosed by plane curves Change of variables in double integrals Area of a curved surface - Triple integrals Volume of Solids.
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