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Unit - 1 Linear Algebra- Matrices

Unit 1Linear Algebra Matrices

1.1 Inverse of a matrix by GaussJordan method Rank of a matrix

1.2 Normal form of a matrix

1.3 Eigen values and Eigen vectors

1.4 Properties of Eigen values and Eigen vectors without proofs

1.5 Cayley Hamilton’s theorem without proof and its applications.

Unit - 2 Partial Differentiation

Unit – 2Partial Differentiation

2.1 a Partial Derivative of first order

2.1 b Partial Derivative of higher order

2.2. Homogeneous function Euler’s theorem for functions containing two and three variables with proofs

2.3. Total Derivatives

2.4. Change of variable

Unit - 3 Applications of Partial differentiation

Unit 3Applications of Partial differentiation

3.1 Jacobians – properties

3.2 Taylor’s and Maclaurin’s theorems without proofs for functions of two variables

3.3 Maxima and minima of functions of two variables

3.4 Lagrange’s method of undetermined multipliers.

Unit - 4 Reduction Formulae and Curve Tracing

UNIT4REDUCTION FORMULAE AND CURVE TRACING

4.1 Reduction formula

Unit - 5 Multiple Integrals

Unit 5Multiple Integrals

5.1 Double integration in Cartesian and polar coordinates

5.2 Evaluation of double integrals by changing the order of integration and changing to polar form

5.3 Triple integral

5.4 Applications of multiple integrals to find area as double integral

5.5 Volume as triple integral and surface area

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