 COURSE SUMMARY
Course Title:
Matrices and Vector Calculus
Course Code:
18MAT118
Year Taught:
2019
Semester:
2
Degree:
Integrated Degree
School:
School of Arts and Sciences
Campus:
Mysuru

'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.

#### Scope and Objectives

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.

#### Syllabus

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).

#### Textbook

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.

#### References

1. Murray R Spiegel, Theory and problems of vector analysis, Schaum’s outline series, McGraw-Hill Book Company 1974.