Physics 6401 - Methods of Theoretical Physics I (Bhuiyan)

Number of Credits: 3
Prerequisites: Permission of the Graduate Committee
Lutful Bari Bhuiyan
Office: C-317 (ext 4775)
University of Puerto Rico - Rio Piedras Campus
Department of Physics

Mathematical Methods for Physicists , 6th edition, George B. Arfken and Hans J. Weber (Elsevier, Academic Press)

Grading will be based on four exams each of which will have the same weight. At least two of the exams will have take home components that need to be handed in within a specified period. The exams will constitute 75% of the total Grade, while the remaining 25% will be based on a numerical project.
Problems in the exams will be based on the material covered in the class, examples worked out in class, suggested problems, and exercises given throughout the course.

Vector analysis
- Brief review of basic concepts, definitions
- Rotation of coordinate axes
- Vector calculus, differential vector operators, Gauss' Divergence Theorem, Stokes' Theorem, potential theory
- Curvilinear coordinates, tensor analysis
Infinite series
- Various convergence tests
- Power series, Taylor's expansion
Functions of a complex variable
- Basic concepts, complex algebra
- Analyticity of a complex function, Cauchy-Riemann conditions
- Cauchy's integral Theorem, Cauchy's integral formula
Exam I
Functions of a complex variable (contd)
- Functions of a complex variable (contd)
- Laurent series, singularities
- Conformal mapping
- Calculus of residues, Residue Theorem
- Evaluation of real integrals using the Residue Theorem
Exam II
Special functions
- Legendre polynomials, Associated Legendre polynomials
- Spherical harmonics
- Bessel functions of the First and Second Kinds, Neuman functions, Hankel functions, Hermite functions
- Gamma and Beta functions, analyticity of Gamma functions
Exam III
Fourier Series and Integrals
- Properties, applications of Fourier series, Dirichlet conditions
- Complex Fourier series
- Development of the Fourier Integral
- Fourier transforms
Green's functions and applications to electromagnetism, waves
Exam IV