Course

Systems of Linear Equations: Linear System of Equations, Gauss Elimination, Consistency of a linear system of equations.

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, Quadratic forms and Canonical form of a quadratic form.

Vector differentiation: Limit of a vector function continuity and derivative of vector function – Geometrical and Physical significance of vector differentiation – Partial derivative of vector function gradient and directional derivative of scalar point functions Equations of tangent plane and normal line to a level surface. Divergence and curl of a vector point function solenoid and irrational functions physical interpretation of divergence and curl of a vector point function.

Integration of vector functions Line, surface and volume integrals. Gauss – Divergence Theorem Greens Theorem Stokes Theorem (Statements only). Verification of theorems and simple problems.

Course Outcomes:

CO1: To Understand the various methods for solving system of linear equations and apply to some physics problems.

CO2: To understand the eigen values and eigen vectors and apply to some problems.

CO3: To learn the scalar and vector fields, gradient, divergence and curl of vector fields and their physical interpretations

CO4: To learn line integral, surface integral and volume integrals. To understand Greens Theorem, Divergence theorem and Stokes theorem.

TEXT BOOKS

1.Advanced Engineering Mathematics, Erwin Kreyszig, John Wiley and Sons, 10th edition, 2023.

2.Vector Calculus with Applications to Physics, Shaw James Byrnie 2009.

3.Advanced Engineering Mathematics by Dennis G. Zill and Michael R.Cullen, second edition, CBS Publishers, 2012.