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Unit - 1 Matrix

UNIT 1Matrix

1.1. Matrix introduction

1.2. Special types of matrices

1.3. Elementary transformation

1.4. Rank of matrix Echelon form Normal form

1.5. Linear system of equations Homogeneous Nonhomogeneous

1.6. Consistency and inconsistency of linear systems

1.7. Characteristic roots and vectors Eigen values Eigen vectors

1.8. CayleyHamilton theorem

1.9. Applications of matrices

Unit - 2 Differential Calculus-I

UNIT 2Differential CalculusI

2.1. Successive differentiation

2.3. Leibnitz’s theorem

2.4. Partial differentiation

2.5. Partial derivatives of first order and higher orders

2.6. Homogeneous functions

2.7. Euler’s theorem on homogeneous functions Relation between second order derivatives of homogeneous functions

2.8. Deductions of Euler’s theorem

2.9. Composite function

2.10. Asymptotes

2.11. Curve tracing Cartesian Polar coordinates

Unit - 3 Differential Calculus-II

UNIT 3Differential CalculusII

3.1. Expansion of functions of several variables Theorems for two variables

3.2. Taylor’s and Maclaurin’s Theorem

3.3. Jacobian Properties of Jacobian

3.4. Jacobian of Implicit functions

3.5. Functional Dependence

3.6. Maxima and minima of functions of two variables

3.7. Lagrange’s Methods of Multipliers

Unit - 4 Multiple Integrals

UNIT 4Multiple Integrals

4.1. Multiple integrals Double and triple

4.2. Change of order of integration

4.3. Change of variables

4.4. Volumes and surface areas by multiple integrals Cartesian and polar coordinates

4.5. Beta and Gamma functions

4.6. Dirichlet’s integrals and extension of Dirichlet’s integrals

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