
B.S. MATHEMATICAL PHYSICSI [PHYS511] SYLLABUS

Vectors in classical physics: Differentiation
of vectors, fields, Directional derivatives and gradients, Line integrals,
Green’s theorem in the Plane, The divergence and divergence theorem,
The Curl and Stoke’s theorem.

Differential equations in Physics: First and Second
order linear differential equations, Homogeneous and Inhomogeneous
solutions, series solution of Differential equations, Partial differential
equations in physics, SturmLiouville systems, introduction to non
linear systems.

Complex variables: Functions of complex variables,
Cauchy Riemann conditions and analytic functions, Cauchy integral
theorem and integral formula, Taylor and Laurent series, Calculus
of residues, Complex integration.

Linear Vector Spaces and Matrices: Linear vector
spaces, Gramschmidt orthogonalization, Matrices, Eigen values and
Eigen vectors of a matrix, Hilbert spaces, Orthogonalization.

Special functions: Bessel functions and Hankel functions,
Spherical Bessel functions, Legendre Polynomials, Associated Legendre
Polynomial, Laugerre Polynomial, Hermite Polynomial.

Integral Transforms: The Laplace transform, Application
of Laplace transform, Fourier transform, Convolution and Parseval’s
theorem, integral transform solution of partial differential equations,
Dirac delta function.

Recommended Text:
1. G. B. Arfken, “Mathematical Methods for Physicists”,
Academic Press Inc. (1995).
2. M. L. Boas, “Mathematical Methods in Physical sciences”,
John Wiley and Sons, New York (1989).
3. P. K. Chattopadhyay, “Mathematical Physics”, Wiley
eastern Limited, New Delhi (1990).
4. H. Cohen, “Mathematics for Scientists and Engineers”,
Prentice Hall international Inc., New Jersey (1992).
5. E. Kreyszig, “Advanced Engineering Mathematics”, John
Wiley and Sons, 7th edition (1993).



