Physics 6401  Methods of Theoretical Physics I (Bhuiyan)
 Number of Credits: 3
 Prerequisites: Permission of the Graduate Committee
 Lutful Bari Bhuiyan

Office: C317 (ext 4775)
University of Puerto Rico  Rio Piedras Campus
Department of Physics
Text
 Mathematical Methods for Physicists , 6th edition, George B. Arfken and Hans J. Weber (Elsevier, Academic Press)
Minimum Required Facilities
 Traditional lecture room
Instructional Strategy
 Lectures
Grading
 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.
Contents

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, CauchyRiemann 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
RIGHTS OF STUDENTS WITH DISABILITIES
ACOMODO RAZONABLE
INTEGRIDAD ACADEMICA