'Matrices and Vector Calculus' is a course offered in Second Semester of B. Sc. - B. Ed. in Physics, Mathematics, Computer Science program at the School of Arts and Sciences, Amrita Vishwa Vidyapeetham, Mysuru campus.
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.
Unit II: 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.