**PH: 301 Methods of Mathematical Physics **

- Review of vector analysis: definitions, rotation of coordinate axes, scalar product, cross product, addition of vectors.
- Differential operators, gradient, divergence, curl, integration of vector fields, Gauss' theorem, Stokes' theorem, Gauss' law, Poisson's equation.
- Definition of delta function, representations including plane wave expansion, generalization to 3 dimensions.
- Vector analysis in curvilinear coordinates, orthogonal coordinates in R3, circular and spherical coordinates, definition of tensors, contraction, direct product, quotient rule, pseudo tensors, dual tensors, tensor derivative operators.
- Determinants, matrices, orthogonal and unitary matrices, matrix diagonalization, trace theorem, relation between determinants and traces.
- Finite and infinite sequences, limit of a sequence.
- Finite and infinite series, tests of convergence, alternating series, algebra of series, series of functions, Taylor's expansion and power series, Bernoulli numbers, Euler-Maclaurin formula, asymptotic series, infinite products
- Fourier series and analysis, use and application to physical systems. orthogonality and orthonormality, complete sets of functions, Gibbs phenomenon, discrete and continuous Fourier transform.
- Complex algebra, functions of a complex variable, Cauchy-Riemann conditions, integration of complex functions, calculus of residues, Cauchy's theorem, Laurent expansion, dispersion relations.

**Recommended Texts:**

*Mathematical Methods for Physicists*, by Arfken & Weber, publisher: Academic Press; 6th Edition, (2005)*Mathematical Methods for Physicists,*by Tai L. Chow, publisher: Cambridge University Press, (2002)*Basic Training in Mathematics: A Fitness Program for Science Students*, R. Shankar, publisher: Springer (1995)