In analytical geometry , a transcendental curve is a curve that is not an algebraic curve. Here for a curve, C, what matters is the point set (typically in the plane) underlying C, not a given parametrisation. For example, the unit circle is an algebraic curve (pedantically, the real points of such a curve); the usual parametrisation by trigonometric functions may involve those transcendental functions, but certainly the unit circle is defined by a polynomial equation. (The same remark applies to elliptic curves and elliptic functions; and in fact to curves of genus > 1 and automorphic functions.) The properties of algebraic curves, such as Bézout's theorem, give rise to criteria for showing curves actually are transcendental. For example an algebraic curve C either meets a given line L in a finite number of points, or possibly contains all of L. Thus a curve intersecting any line in an infinite number of points, while not containing it, must be transcendental. This applies not just to sinusoidal curves, therefore; but to large classes of curves showing oscillations. The term is originally attributed to Leibniz. (Wikipedia).
Transcendental Functions 14 Derivative of Natural Log of x Example 3.mov
More examples to work through.
From playlist Transcendental Functions
Transcendental Functions 14 Derivative of Natural Log of x.mov
The first derivative of the natural log of x.
From playlist Transcendental Functions
Transcendental Functions 18 More Examples 1.mov
More example problems.
From playlist Transcendental Functions
Transcendental Functions 18 More Examples 2.mov
More example problems.
From playlist Transcendental Functions
Transcendental Functions 13 Derivatives of a Function and its Inverse.mov
The first derivative of a function and the inverse of that function.
From playlist Transcendental Functions
Transcendental Functions 1 Introduction.mov
Transcendental Functions in Calculus.
From playlist Transcendental Functions
Transcendental Functions 21 The Derivative of e to the power x.mp4
The derivative of e to the power x.
From playlist Transcendental Functions
Transcendental Functions 9 One More Property of Logarithms.mov
Another logarithmic property.
From playlist Transcendental Functions
Transcendental Functions 19 The Function a to the power x.mp4
The function a to the power x.
From playlist Transcendental Functions
Anna Miriam Benini: Polynomial versus transcendental dynamics
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 24, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Dynamical Systems and Ordinary Differential Equations
Jacob Tsimerman, Unlikely intersections and the André-Oort conjecture
VaNTAGe Seminar, December 7, 2021 License: CC-BY-NC-SA
From playlist Complex multiplication and reduction of curves and abelian varieties
Yuri Manin - Numbers as functions
Numbers as functions
From playlist 28ème Journées Arithmétiques 2013
Galois theory: Transcendental extensions
This lecture is part of an online graduate course on Galois theory. We describe transcendental extension of fields and transcendence bases. As applications we classify algebraically closed fields and show hw to define the dimension of an algebraic variety.
From playlist Galois theory
Title: Algebraic Independence of Functions Satisfying Nonlinear Polynomial Mahler Equations
From playlist Differential Algebra and Related Topics VII (2016)
Charlotte Hardouin: Galois theory and walks in the quarter plane
Abstract: In the recent years, the nature of the generating series of walks in the quarter plane has attracted the attention of many authors in combinatorics and probability. The main questions are: are they algebraic, holonomic (solutions of linear differential equations) or at least hype
From playlist Combinatorics
Title: Density of Rational Points on Transcendental Varieties
From playlist Differential Algebra and Related Topics VII (2016)
Kirill Lazebnik: Transcendental Julia sets of minimal Hausdorff dimension
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 21, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Analysis and its Applications
David Martí-Pete: Wandering lakes of Wada
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 20, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM'
From playlist Analysis and its Applications
Transcendental Functions 16 Proof of the Properties of Logarithms Part 1.mov
Proof of some of the properties of logarithms.
From playlist Transcendental Functions
Hodge theory, between algebraicity and transcendence (Lecture 2) by Bruno Klingler
DISCUSSION MEETING TOPICS IN HODGE THEORY (HYBRID) ORGANIZERS: Indranil Biswas (TIFR, Mumbai, India) and Mahan Mj (TIFR, Mumbai, India) DATE: 20 February 2023 to 25 February 2023 VENUE: Ramanujan Lecture Hall and Online This is a followup discussion meeting on complex and algebraic ge
From playlist Topics in Hodge Theory - 2023