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

'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.

On completion of the course, the student teacher will;

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.