Curves

Transcendental curve

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).

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Transcendental Functions 14 Derivative of Natural Log of x.mov

The first derivative of the natural log of x.

From playlist Transcendental Functions

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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

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Transcendental Functions 1 Introduction.mov

Transcendental Functions in Calculus.

From playlist Transcendental Functions

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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

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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

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DART VII Thomas Scanlon

Title: Algebraic Independence of Functions Satisfying Nonlinear Polynomial Mahler Equations

From playlist Differential Algebra and Related Topics VII (2016)

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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

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DART VII Gal Binyamini

Title: Density of Rational Points on Transcendental Varieties

From playlist Differential Algebra and Related Topics VII (2016)

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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

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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

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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

Related pages

Automorphic function | Bézout's theorem | Algebraic curve | Elliptic curve | Gottfried Wilhelm Leibniz | Unit circle | Elliptic function | Curve | Transcendental function | Exponential function | Cycloid | Catenary | Genus (mathematics) | Logarithm | Logarithmic spiral