Lecture 1 - Genesis and a little history
Lecture 2 - Basic convergence theorem
Lecture 3 - Riemann Lebesgue Lemma
Lecture 4 - The ubiquitous Gaussian
Lecture 5 - Jacobi theta function identity
Lecture 6 - The Riemann zeta function
Lecture 7 - Bessel's functions of the first kind
Lecture 8 - Least square approximation
Lecture 9 - Parseval formula. Isoperimetric theorem
Lecture 10 - Dirichlet problem for a disc
Lecture 11 - The Poisson kernel
Lecture 12 - Cesaro summability and Fejer's theorem
Lecture 13 - Fejer's theorem (Continued...)
Lecture 14 - Kronecker's theorem
Lecture 15 - Weyl's equidistribution theorem
Lecture 16 - Borel's theorem and beyond
Lecture 17 - Fourier transform and Schwartz space
Lecture 18 - Hermite's differential equation
Lecture 19 - Fourier inversion theorem Riemann Lebesgue lemma
Lecture 20 - Plancherel's Theorem
Lecture 21 - Heat equation. The heat kernel
Lecture 22 - The Airy's function
Lecture 23 - Exercises on Fourier Transform
Lecture 24 - Principle of equipartitioning of energy
Lecture 25 - A formula of Srinivasa Ramanujan
Lecture 26 - Sturm Liouville problems. Orthogonal systems
Lecture 27 - Vibrations of a circular membrane
Lecture 28 - Fourier Bessel Series
Lecture 29 - Properties of Legendre Polynomials
Lecture 30 - Properties of Legendre polynomials (Continued...)
Lecture 31 - Legendre polynomials - interlacing of zeros
Lecture 32 - Laplace's integrals for Legendre polynomials
Lecture 33 - Regular Sturm-Liouville problems
Lecture 34 - Variational properties of eigen-values
Lecture 35 - The Dirichlet principle
Lecture 36 - Regular Sturm-Liouville problems - Existence of eigen-values
Lecture 37 - The Bergman space
Lecture 38 - The Banach Steinhaus' Theorem
Lecture 39 - Hilbert space basics
Lecture 40 - Completeness of Hermite functions
Lecture 41 - Hermite, Laugerre and Tchebycheff's polynomials
Lecture 42 - Orthonormal bases in Hilbert spaces
Lecture 43 - Non-separable Hilbert-spaces. Almost periodic functions
Lecture 44 - Hilbert-Schmidt operators. Green's functions
Lecture 45 - Spectrum of a bounded linear operator
Lecture 46 - Weak (sequential) compactness of the closed unit ball
Lecture 47 - Compact self-adjoint operators. Existence of eigen values
Lecture 48 - Compact self-adjoint operators. Existence of eigen values (Continued...)
Lecture 49 - Celestial Mechanics
Lecture 50 - Inverting the Kepler equation using Fourier series
Lecture 51 - Odds and Ends
Lecture 52 - Dirichlet's Theorem on Fourier Series
Lecture 53 - Dirichlet's Theorem on Fourier Series (Continued...)
Lecture 54 - Topology on the Schwartz space
Lecture 55 - Examples of tempered distributions
Lecture 56 - Operations on distributions
Lecture 57 - Fourier Transform of tempered distribution
Lecture 58 - Support of a Distribution. Distributions with point support
Lecture 59 - Distributional solutions of ODEs. Continuity of the Fourier transform and differentiation
Lecture 60 - The Poisson summation formula
