PHYS 5110 - Mathematical Methods in Physics

Teaching Pattern

• Duration of course: about 13 weeks

• Lecture hour(s) per week: 4

Content

• Review of vector analysis
• Complex variable theory, Cauchy-Rieman conditions, complex Taylor and Laurent series, Cauchy integral formula and residue techniques, conformal mapping
• Fourier series
• Fourier and Laplace transforms
• Ordinary differential equations, Bessel functions
• Partial differential equations, wave and diffusion equations, Laplace, Helmholtz and Poisson's equations, transform techniques, Green's functions
• Integral equations, Fredholm equations, kernals
• Rieman sheets, method of steepest descent
• Tensors, contravariant and covariant representations
• Group theory, matrix representations