Systems of Linear Equations: Linear System of Equations, Gauss Elimination, Consistency of a linear system of equations, Vectors, Linear independence and dependence of vectors, Rank of a Matrix.
Text Book-1: Chapter-1 and 2
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, Power of a matrix, Diagonalization by orthogonal transformation, Quadratic forms, Canonical form of a quadratic form, Nature of quadratic forms.
Text Book-1: Chapter-7.
Three dimensional coordinate systems, vectors, dot and cross products. Vector Differentiation: Gradient, divergence and curl, identities, invariant scalar.
Text Book-2: Chapter-12 (Sections 12.1-12.5)
Line integrals, Vector Fields, Work, Circulation an ,and Flux, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the plane.
Text Book-2: Chapter-16 (Sections 16.1-16.4)
Surface area and surface integrals, Parametrized surfaces, Stokes Theorem, The divergence Theorem and a unified theory.
Text Book-2: Chapter-16 (Sections 16.5-16.8)