# InfoCoBuild

## 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 18 - Laplace Transforms (Part I)

Definition of the Laplace transform. The convolution theorem. Laplace transforms of derivatives. The inverse transform, Mellin's formula. The LCR series circuit. Laplace transform of the Bessel and modified Bessel functions of the first kind. Laplace transforms and random processes: the Poisson process.

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) 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)