An example of expanding a function in a Legendre-Fourier Series.
From playlist Mathematical Physics II Uploads
An introduction to Legendre Polynomials and the Legendre-Fourier Series.
From playlist Mathematical Physics II Uploads
In this video I derive three series representations for Legendre Polynomials. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F
From playlist Fourier
Constructing the Legendre polynomials, which are an orthonormal basis for the set of polynomials. Example of Gram-Schmidt to inner product spaces. Check out my Orthogonality playlist: https://www.youtube.com/watch?v=Z8ceNvUgI4Q&list=PLJb1qAQIrmmAreTtzhE6MuJhAhwYYo_a9 Subscribe to my chan
From playlist Fourier
The Fourier Transform and Derivatives
This video describes how the Fourier Transform can be used to accurately and efficiently compute derivatives, with implications for the numerical solution of differential equations. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow
From playlist Fourier
In this video I briefly introduce Legendre Polynomials via the Rodrigues formula. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F
From playlist Fourier
Introduction to the z-Transform
http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Introduces the definition of the z-transform, the complex plane, and the relationship between the z-transform and the discrete-time Fourier transfor
From playlist The z-Transform
Umberto Zannier - Torsion values for sections in abelian schemes and the Betti map
November 14, 2017 - This is the second of three Fall 2017 Minerva Lectures We shall consider further variations in the games, obtaining more general Betti maps. We shall also illustrate some links of the Betti map with several other contexts (Manin's theorem of the kernel, linear different
From playlist Minerva Lectures Umberto Zannier
Shiri Artstein-Avidan: On optimal transport with respect to non traditional costs
Shiri Artstein-Avidan (University of Tel Aviv) On optimal transport with respect to non traditional costs After a short review of the topic of optimal transport, introducing the c-transform and c-subgradients, we will dive into the intricacies of transportation with respect to a cost wh
From playlist Trimester Seminar Series on the Interplay between High-Dimensional Geometry and Probability
On the (in)stability of the identity map in optimal transportation - Yash Jhaveri
Analysis Seminar Topic: On the (in)stability of the identity map in optimal transportation Speaker: Yash Jhaveri Affiliation: Member, School of Mathematics Date: October 14, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Joscha Prochno: The large deviations approach to high-dimensional convex bodies, Lecture I
Given any isotropic convex body in high dimension, it is known that its typical random projections will be approximately standard Gaussian. The universality in this central limit perspective restricts the information that can be retrieved from the lower-dimensional projections. In contrast
From playlist Workshop: High dimensional spatial random systems
Richard Kraaij: A Lagrangian formalism for large deviations of independent copies...
Richard Kraaij: A Lagrangian formalism for large deviations of independent copies of Feller processes Dawson and Gaertner (1987) showed that the path of the empirical process of n independent identically distributed diffusion processes satisfy a large deviation principle in n with a rate
From playlist HIM Lectures 2015
Noether’s Theorem in Classical Dynamics : Continuous Symmetries by N. Mukunda
DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (
From playlist The Legacy of Emmy Noether
Finite Difference Method for finding roots of functions including an example and visual representation. Also includes discussions of Forward, Backward, and Central Finite Difference as well as overview of higher order versions of Finite Difference. Chapters 0:00 Intro 0:04 Secant Method R
From playlist Root Finding
Dynamics and transport in integrable and nearly integrable models (Lecture 3) by Joel Moore
PROGRAM: INTEGRABLE SYSTEMS IN MATHEMATICS, CONDENSED MATTER AND STATISTICAL PHYSICS ORGANIZERS: Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE : 16 July 2018 to 10 August 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
Sums of Squares and Golden Gates - Peter Sarnak (Princeton)
Through the works of Fermat, Gauss, and Lagrange, we understand which positive integers can be represented as sums of two, three, or four squares. Hilbert's 11th problem, from 1900, extends this question to more general quadratic equations. While much progress has been made since its formu
From playlist Mathematics Research Center
What is the Fourier Transform?
In this video, we'll look at the fourier transform from a slightly different perspective than normal, and see how it can be used to estimate functions. Learn about the Fourier series here: http://youtu.be/kP02nBNtjrU
From playlist Fourier
Fourier Transform Technique for Solving PDEs (Part 1)
In this video, we look at some of the properties of the Fourier Transform (Linearity and Derivatives), and set up a PDE problem that we will solve using the Fourier Transform technique.
From playlist Mathematical Physics II Uploads
K-groups and Global Fields by Haiyan Zhou
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture