Selected Topics in Mathematical Physics (V. Balakrishnan, IIT Madras): Lecture 03

Selected Topics in Mathematical Physics

Selected Topics in Mathematical Physics. Instructor: Professor V. Balakrishnan, Department of Physics, IIT Madras. A basic course in mathematical methods used in physics. Analytic functions of a complex variable. Calculus of residues, Linear response; dispersion relations. Analytic continuation and the gamma function. Mobius transformations. Multivalued functions; integral representations. Laplace transforms. Fourier transforms. Fundamental Green function for the Laplacian operator. The diffusion equation. Green function for the Helmholtz operator; nonrelativistic scattering. The wave equation. The rotation group and all that. (from nptel.ac.in)

Lecture 03 - Calculus of Residues (Part I)

Cauchy's integral theorem. Singularities, removable singularity, simple pole, multiple pole, essential singularity. Laurent series. Singularity at infinity. Accumulation point of poles. Meromorphic functions. Cauchy's integral formula.

Go to the Course Home or watch other lectures:

Lecture 01 - Analytic Functions of a Complex Variable (Part I)

Lecture 02 - Analytic Functions of a Complex Variable (Part II)

Lecture 03 - Calculus of Residues (Part I)

Lecture 04 - Calculus of Residues (Part II)

Lecture 05 - Calculus of Residues (Part III)

Lecture 06 - Calculus of Residues (Part IV)

Lecture 07 - Linear Response; Dispersion Relations (Part I)

Lecture 08 - Linear Response; Dispersion Relations (Part II)

Lecture 09 - Analytic Continuation and the Gamma Function (Part I)

Lecture 10 - Analytic Continuation and the Gamma Function (Part II)

Lecture 11 - Mobius Transformations (Part I)