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UNIT I MATRICES

1.1 Eigen values and Eigen vectors of a real matrix

1.2 Characteristic equation

1.3 Properties of eigenvalues and eigenvectors

1.4 Statement and applications of Cayley - Hamilton Theorem

1.5 Diagonalization of matrices

1.6 Reduction of a quadratic form to canonical form by orthogonal transformation

1.7 Nature of quadratic forms

UNIT II SEQUENCES AND SERIES

2.1 Sequences

2.2 Series

2.3 Series of positive terms

2.4 Tests of convergence

2.5 Alternating series

2.6 Leibnitz‟s test

2.7 Series of positive and negative terms

2.8 Absolute and conditional convergence

UNIT III APPLICATIONS OF DIFFERENTIAL CALCULUS

3.1 Curvature in Cartesian co-ordinates

3.2 Centre and radius of curvature

3.3 Circle of curvature

3.4 Evolutes

3.5 Envelopes

3.6 Evolute as envelope of normals

UNIT IV DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES

4.1 Limits and Continuity

4.2 Partial derivatives

4.3 Total derivative

4.4 Differentiation of implicit functions

4.5 Jacobian and properties

4.6 Taylor‟s series for functions of two variables

4.7 Maxima and minima of functions of two variables

4.8 Lagrange‟s method of undetermined multipliers.

UNIT V MULTIPLE INTEGRALS

5.1 Double integrals in Cartesian and polar coordinates

5.2 Change of order of integration

5.3 Area enclosed by plane curves

5.4 Change of variables in double integrals

5.5 Area of a curved surface

5.6 Triple integrals

5.7 Volume of Solids