Elliptic functions | Jacobi elliptic functions | Special functions
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation for . The Jacobi elliptic functions are used more often in practical problems than the Weierstrass elliptic functions as they do not require notions of complex analysis to be defined and/or understood. They were introduced by Carl Gustav Jakob Jacobi. Carl Friedrich Gauss had already studied special Jacobi elliptic functions in 1797, the lemniscate elliptic functions in particular, but his work was published much later. (Wikipedia).
Etale Theta - Part 02 - Properties of the Arithmetic Jacobi Theta Function
In this video we talk about Proposition 1.4 of Etale Theta. This came out of conversations with Emmanuel Lepage. Formal schemes in the Stacks Project: http://stacks.math.columbia.edu/tag/0AIL
From playlist Etale Theta
Gentle example showing how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
An introduction to how the jacobian matrix represents what a multivariable function looks like locally, as a linear transformation.
From playlist Multivariable calculus
Gentle example explaining how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
Jacobian chain rule and inverse function theorem
A lecture that discusses: the general chain rule for the Jacobian derivative; and the inverse function theorem. The concepts are illustrated via examples and are seen in university mathematics.
From playlist Several Variable Calculus / Vector Calculus
The J function, sl(2) and the Jacobi identity | Universal Hyperbolic Geometry 19 | NJ Wildberger
We review the basic connection between hyperbolic points and matrices, and connect the J function, which computes the joins of points or the meets of lines, with the Lie bracket of 2x2 matrices. This connects with the Lie algebra called sl(2) in the projective setting. The Jacobi identity
From playlist Universal Hyperbolic Geometry
Jim Bryan : Curve counting on abelian surfaces and threefolds
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
What's New in Calculus and Algebra
This talk features Devendra Kapadia, who summarizes recent developments related to calculus and algebra in the Wolfram Language. These developments include state-of-the-art algorithms for computing inverse Laplace transforms and working with holonomic functions, new elliptic and Lamé speci
From playlist Wolfram Technology Conference 2020
Newton's Method for Systems of Nonlinear Equations
Generalized Newton's method for systems of nonlinear equations. Lesson goes over numerically solving multivariable nonlinear equations step-by-step with visual examples and explanation of the Jacobian, the backslash operator, and the inverse Jacobian. Example code in MATLAB / GNU Octave on
From playlist Newton's Method
Sander Zwegers: Fourier coefficients of meromorphic Jacobi forms
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.
Intro to Jacobian + differentiability
A lecture that introduces the Jacobian matrix and its determinant. Such ideas may be thought of as a general derivative of a vector-valued function of many variables and find uses in integration theory.
From playlist Several Variable Calculus / Vector Calculus
Complex analysis: Elliptic functions
This lecture is part of an online undergraduate course on complex analysis. We start the study of elliptic (doubly periodic) functions by constructing some examples, and finding some conditions that their poles and zeros must satisfy. For the other lectures in the course see https://www
From playlist Complex analysis
Modularity of Elliptic Curves | Math PhDs Outside Academia (Jeff Breeding-Allison) | Ep. 11
Jeff Breeding-Allison is a number theorist and a professional data scientist. We discuss Jeff's work in number theory, and I ask him about they key steps in the proof that elliptic curves are modular (the result that proved Fermat's Last Theorem). Then we discuss Jeff's transition out of a
From playlist Daniel Rubin Show, Full episodes
Pierre Louis Lions - Tribute to Ennio De Giorgi - 19 September 2016
Lions , Pierre Louis "Interfaces, junctions and stratification: a viscosity solutions approach"
From playlist A Mathematical Tribute to Ennio De Giorgi
George Papanicolaou: Stochastic Analysis in Finance
This lecture was held at The University of Oslo, May 24, 2007 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2007 1. “A Short History of Large Deviations” by Srinivasa Varadhan, Abel Laureate 2007, Courant Ins
From playlist Abel Lectures
Elliptic genera of Pfaffian-Grassmannian double mirrors - Lev Borisov
Lev Borisov Rutgers University November 5, 2014 More videos on http://video.ias.edu
From playlist Mathematics
A Converse to a Theorem of Gross-Zaqier-Kolyvagin - Christopher Skinner
Christopher Skinner Princeton University; Member, School of Mathematics April 4, 2013 The theorem of the title is that if the L-function L(E,s) of an elliptic curve E over the rationals vanishes to order r=0 or 1 at s=1 then the rank of the group of rational rational points of E equals r a
From playlist Mathematics
Approximating the Jacobian: Finite Difference Method for Systems of Nonlinear Equations
Generalized Finite Difference Method for Simultaneous Nonlinear Systems by approximating the Jacobian using the limit of partial derivatives with the forward finite difference. Example code on GitHub https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:13 Prerequisites 0:3
From playlist Solving Systems of Nonlinear Equations
Boris Pioline : A string theorist view point on the genus-two Kawazumi-Zhang invariant
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Number Theory