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Unit - 1 Matrix Operations and Solving Systems of Linear Equations

Unit 1Matrix operations and solving systems of linear equations

1.1 Rank of a matrix by echelon form

1.2 Solving system of homogeneous and non – homogenous equations Linear equations

1.3 Eigen values and eigen vectors and their properties

1.4 Cayley – Hamilton theorem without proof

1.5 Finding inverse and power of a matrix by Cayley – Hamilton theorem

1.6 Diagonalisation of a matrix

1.7 Quadratic forms and nature of the quadratic forms

1.8 Reduction of quadratic form to canonical forms by orthogonal transformation

Unit - 2 Mean Value Theorems

Unit 2Mean value theorems

2.1 Rolle’s theorem

2.2 Lagrange’s mean value theorem

2.3 Cauchy’s mean value theorem

2.4 Taylor’s and Maclaurin theorems with remainders without proof

Unit - 3 Multivariable calculus

Unit 3Multivariable calculus

3.1 Partial derivatives

3.2 Total derivatives

3.3 Chain rule

3.4 Change of variables

3.5 Jacobians

3.6 Maxima and minima of function of two variables

3.7 Method of Lagrange multipliers

Unit - 4 Double Integrals

Unit 4Double Integral

4.1 Double integrals

4.2 Change of order integration

4.3 Double integration in polar coordinates

4.4 Areas enclosed by plane curves

Unit 4

Double Integral

4.1 Double integrals

4.2 Change of order integration

4.3 Double integration in polar coordinates

4.4 Areas enclosed by plane curves

Unit - 5 Multiple Integrals and Special Functions

Unit 5Multiple Integral and special function

5.1 Evaluation of triple integrals

5.2 Change of variables between Cartesian to polar

5.3 Cylinder and spherical polar coordinates

5.4 Beta and Gamma functions and their properties

5.5 Relation between beta and gamma functions

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