'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.
B. Tech. (Bachelor of Technology) in Electronics and Communication Engineering, B. Tech. (Bachelor of Technology) in Electrical and Electronics Engineering, B. Tech. (Bachelor of Technology) in Computer and Communication Engineering, B. Tech. (Bachelor of Technology) in Civil Engineering