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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 06 - Calculus of Residues (Part IV)

Contour integration. Mittag-Leffler expansions of meromorphic functions.

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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)

Lecture 12 - Mobius Transformations (Part II)

Lecture 13 - Mobius Transformations (Part III)

Lecture 14 - Multivalued Functions; Integral Representations (Part I)

Lecture 15 - Multivalued Functions; Integral Representations (Part II)

Lecture 16 - Multivalued Functions; Integral Representations (Part III)

Lecture 17 - Multivalued Functions; Integral Representations (Part IV)

Lecture 18 - Laplace Transforms (Part I)

Lecture 19 - Laplace Transforms (Part II)

Lecture 20 - Fourier Transforms (Part I)

Lecture 21 - Fourier Transforms (Part II)

Lecture 22 - Fourier Transforms (Part III)

Lecture 23 - Fundamental Green Function for Δ² (Part I)

Lecture 24 - Fundamental Green Function for Δ² (Part II)

Lecture 25 - The Diffusion Equation (Part I)

Lecture 26 - The Diffusion Equation (Part II)

Lecture 27 - The Diffusion Equation (Part III)

Lecture 28 - The Diffusion Equation (Part IV)

Lecture 29 - Green function for (Δ² + k²); Nonrelativistic Scattering (Part I)

Lecture 30 - Green function for (Δ² + k²); Nonrelativistic Scattering (Part II)

Lecture 31 - Green function for (Δ² + k²); Nonrelativistic Scattering (Part III)

Lecture 32 - The Wave Equation (Part I)

Lecture 33 - The Wave Equation (Part II)

Lecture 34 - The Rotation Group and All That (Part I)

Lecture 35 - The Rotation Group and All That (Part II)

Lecture 36 - The Rotation Group and All That (Part III)