In mathematics, synthetic differential geometry is a formalization of the theory of differential geometry in the language of topos theory. There are several insights that allow for such a reformulation. The first is that most of the analytic data for describing the class of smooth manifolds can be encoded into certain fibre bundles on manifolds: namely bundles of jets (see also jet bundle). The second insight is that the operation of assigning a bundle of jets to a smooth manifold is functorial in nature. The third insight is that over a certain category, these are representable functors. Furthermore, their representatives are related to the algebras of dual numbers, so that smooth infinitesimal analysis may be used. Synthetic differential geometry can serve as a platform for formulating certain otherwise obscure or confusing notions from differential geometry. For example, the meaning of what it means to be natural (or invariant) has a particularly simple expression, even though the formulation in classical differential geometry may be quite difficult. (Wikipedia).
Classical curves | Differential Geometry 1 | NJ Wildberger
The first lecture of a beginner's course on Differential Geometry! Given by Prof N J Wildberger of the School of Mathematics and Statistics at UNSW. Differential geometry is the application of calculus and analytic geometry to the study of curves and surfaces, and has numerous applications
From playlist Differential Geometry
Introduction to Differential Equations
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to Differential Equations - The types of differential equations, ordinary versus partial. - How to find the order of a differential equation.
From playlist Differential Equations
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From playlist Popular Questions
Solve the general solution for differentiable equation with trig
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
Infinitesimals in Synthetic Differential Geometry
In this video I describe the logic of Synthetic Differential Geometry. This is a non-constructive theory collapsing in the presence of the law of excluded middle. As a logic al theory, it can be realized in a topos and it has sheave models giving a nice representation of tangent bundles.
From playlist Algebra
Introduction to Differential Equation Terminology
This video defines a differential equation and then classifies differential equations by type, order, and linearity. Search Library at http://mathispower4u.wordpress.com
From playlist Introduction to Differential Equations
The differential calculus for curves, via Lagrange! | Differential Geometry 4 | NJ Wildberger
We rejuvenate the powerful algebraic approach to calculus that goes back to the work of Newton, Euler and particularly Lagrange, in his 1797 book: The Theory of Analytic Functions (english translation). The idea is to study a polynomial function p(x) by using translation and truncation to
From playlist Differential Geometry
Find the particular solution given the conditions and second derivative
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
Symplectic geometry of surface group representations - William Goldman
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GPDE Workshop - Synthetic formulations - Cedric Villani
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In search of quantum geometry by Pranav Pandit
COLLOQUIUM IN SEARCH OF QUANTUM GEOMETRY SPEAKER: Pranav Pandit (ICTS - TIFR, Bengaluru) DATE: Mon, 29 November 2021, 15:30 to 17:00 VENUE: Online and Ramanujan Lecture Hall RESOURCES ABSTRACT Notions of geometry have evolved throughout the history of mathematics, often in parallel
From playlist ICTS Colloquia
Lagrangians, symplectomorphisms and zeroes of moment maps - Yann Rollin
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The differential calculus for curves (II) | Differential Geometry 8 | NJ Wildberger
In this video we extend Lagrange's approach to the differential calculus to the case of algebraic curves. This means we can study tangent lines, tangent conics and so on to a general curve of the form p(x,y)=0; this includes the situation y=f(x) as a special case. It also allows us to deal
From playlist Differential Geometry
Winter School JTP: Introduction to Fukaya categories, James Pascaleff, Lecture 1
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Geometry Of The Hitchin Integrable Systems, And Some Variations (Lecture 2) by Jacques Hurtubise
PROGRAM : QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS : Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
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Floer Theory on Complex-Symplectic Manifolds - Semon Kirillovich Rezchikov
Short Talks by Postdoctoral Members Topic: Floer Theory on Complex-Symplectic Manifolds Speaker: Semon Kirillovich Rezchikov Affiliation: Member, School of Mathematics Date: September 22, 2022
From playlist Mathematics
Partial Derivatives and the Gradient of a Function
We've introduced the differential operator before, during a few of our calculus lessons. But now we will be using this operator more and more over the prime symbol we are used to when describing differentiation, as from now on we will frequently be differentiating with respect to a specifi
From playlist Mathematics (All Of It)
Filiz Dogru: Outer Billiards: A Comparison Between Affine, Hyperbolic, and Symplectic Geometry
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From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022