ALGEBRA, VECTOR ANALYSIS & GEOMETRY

1.1 Historical background :

1.1.1 Development of Indian Mathematics

Later Classical Period (500-1250)

1.1.2 A brief biography of Varahamihira and Aryabhatta

1.2 Rank of Matrix

1.3 Echelon and normal form of matrix

1.4 Characteristic equations of a matrix

1.4.1 Eigen-values

1.4.2 Eigen-vectors

Unit-II

2.1 Cayley Hamilton theorem

2.2 Application of Cayley Hamilton theorem to find the inverse of a matrix

2.3 Application of matrix to solve a system of linear equations

2.4 Theorems on consistency and inconsistency of a system of linear equations

2.5 Solving linear equations up to three unknowns

Unit-III

3.1 Scalar and Vector products of three and four vectors

3.2 Reciprocal vectors

3.3 Vector differentiation

3.3.1 Rules of differentiation

3.3.2 Derivatives of Triple Products

3.4 Gradient, Divergence and Curl

3.5 Directional derivatives

3.6 Vector Identities

3.7 Vector Equations

Unit-IV

4.1 Vector Integration

4.2 Gauss theorem (without proof) and problems based on it

4.3 Green theorem (without proof) and problems based on it

4.4 Stoke theorem (without prof) and problems based on it

Unit-V

5.1 General equation of second degree

5.2 Tracing of conics

5.3 System of conics

5.4 Cone

5.4.1 Equation of cone with given base

5.4.2 Generators of cone

5.4.3 Condition for three mutually perpendicular gerators

5.4.5 Right circular cone

5.5 Cylinder

5.5.1 Equation of cylinder and its properties

5.5.2 Right Circular Cylinder

5.5.3 Enveloping Cylinder