Unit 1

Matrices: Matrix, Algebraic operations, Transpose of a matrix, Inverse of a matrix, Properties of matrices, Kinds of matrices: Symmetric and skew symmetric matrices, Hermitian and skew Hermitian matrices, Orthogonal and unitary matrices, Determinant of a matrix, Properties of determinants.

Unit 2

Systems of Linear Equations: Linear System of Equations, Gauss Elimination, Consistency of a linear system of equations.

Unit 3

Eigen value problems: Eigen values, Eigen vectors, Properties of Eigen values and Eigen vectors, Cayley-Hamilton theorem, Some Applications of Eigen value Problems, Similarity of Matrices, Diagonalization of a matrix, Quadratic forms and Canonical form of a quadratic form.

Unit 4

Vector differentiation: Limit of a vector function – continuity and derivative of vector function – Geometrical and Physical significance of vector differentiation – Partial derivative of vector function – gradient and directional derivative of scalar point functions – Equations of tangent plane and normal line to a level surface. Divergence and curl of a vector point function – solenoid and irrational functions – physical interpretation of divergence and curl of a vector point function.

Unit 5

Integration of vector functions – Line, surface and volume integrals. Gauss – Divergence Theorem – Green’s Theorem – Stoke’s Theorem (Statements only). Verification of theorems and simple problems.

1. ‘Advanced Engineering Mathematics’, Erwin Kreyszig, John Wiley and Sons, 2002, 8th Edition.
2. Textbook of Matrix Algebra, Suddhendu Biswas, PHI, 2012.
3. Vector Calculus with Applications to Physics, Shaw James Byrnie – 2009
4. T. K. Manickavasakam Pillay, Vector Calculus, 2004.