Course Title: 
Matrices and Vector Calculus
Course Code: 
Year Taught: 
Integrated Degree
Undergraduate (UG)
School of Arts and Sciences

'Matrices and Vector Calculus' is a course offered at the School of Arts and Sciences, Amrita Vishwa Vidyapeetham, Mysuru campus.

To enable students to understand the basic concepts of matrix calculus, vectors and basic vector operations and solve computational problems of vector calculus.

Unit I:

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

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.

Unit III:

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)

Unit IV:

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)

Unit V:

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)

  1. Elementary Linear Algebra’, Howard Anton and Chris Rorres, John Wiley & Sons, 1994, Seventh Edition.
  2. Calculus by Finney and Thomas, Pearson, Eleventh Edition, 11th Edition, Pearson, 2009.
  1. Murray R Spiegel, Theory and problems of vector analysis, Schaum’s outline series, McGraw-Hill Book Company 1974.