Algebraic geometry | Complex manifolds
In mathematics, differential of the first kind is a traditional term used in the theories of Riemann surfaces (more generally, complex manifolds) and algebraic curves (more generally, algebraic varieties), for everywhere-regular differential 1-forms. Given a complex manifold M, a differential of the first kind ω is therefore the same thing as a 1-form that is everywhere holomorphic; on an algebraic variety V that is non-singular it would be a global section of the coherent sheaf Ω1 of Kähler differentials. In either case the definition has its origins in the theory of abelian integrals. The dimension of the space of differentials of the first kind, by means of this identification, is the Hodge number h1,0. The differentials of the first kind, when integrated along paths, give rise to integrals that generalise the elliptic integrals to all curves over the complex numbers. They include for example the hyperelliptic integrals of type where Q is a square-free polynomial of any given degree > 4. The allowable power k has to be determined by analysis of the possible pole at the point at infinity on the corresponding hyperelliptic curve. When this is done, one finds that the condition is k ≤ g − 1, or in other words, k at most 1 for degree of Q 5 or 6, at most 2 for degree 7 or 8, and so on (as g = [(1+ deg Q)/2]). Quite generally, as this example illustrates, for a compact Riemann surface or algebraic curve, the Hodge number is the genus g. For the case of algebraic surfaces, this is the quantity known classically as the irregularity q. It is also, in general, the dimension of the Albanese variety, which takes the place of the Jacobian variety. (Wikipedia).
Differential Equations: Linear First Order DEs Introduction
The second of the three analytic methods for solving first order differential equations is only valid if the differential equation is linear. In this video, we look at what it means for a differential equation to be linear and how it can then be solved.
From playlist Differential Equations
Solve a First-Order Homogeneous Differential Equation in Differential Form - Part 1
This video provides an example how to to solve a homogeneous differential equation in differential form. This is part 1 of 3. Site: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist First Order Homogeneous Differential Equations
Differential Equations: First Order Linear Example 2
We present a solution to a first order linear differential equation.
From playlist First Order Linear Differential Equations
Differential Equation - 1st Order Solutions (1 of 8) Separation of Variables: Example 1
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the 1st order solution to 2yy'+3x=0. Next video in the 1st Order Solutions series can be seen at: http://youtu.be/jE0RbFbeQeA
From playlist DIFFERENTIAL EQUATIONS 2 - 1ST ORDER SEPARATION OF VARIABLES
Differential Equation - Introduction (12 of 15) Types 1, 2, 3 of First Order Differential Equations
Visit http://ilectureonline.com for more math and science lectures! In this video I will list (part 1) types 1, 2, 3 of 1st order differential equations where each type requires a specific method to solve that type of differential equation. Next video in the Introduction series can be se
From playlist DIFFERENTIAL EQUATIONS 1 - INTRODUCTION
First Order Linear Equations: Differential Equations Lesson #2
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From playlist Differential Equations
Differential Equations | First Order Linear System of DEs.
We solve a nonhomogeneous system of first order linear differential equations using a strategy inspired from solving a single first order linear differential equation. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Systems of Differential Equations
Determine if a First-Order Differential Equation is Homogeneous - Part 1
This video explains how to determine if a given linear first order differential equation is homogeneous using the ratio definition. Website: http://mathispower4u.com
From playlist First Order Homogeneous Differential Equations
Differential Equations: First Order Linear Example 1
We present a solution to a first order linear differential equation.
From playlist First Order Linear Differential Equations
Differentiation (Part 2 Special Examples) | Revision for Maths A-Level and IB
I want to help you achieve the grades you (and I) know you are capable of; these grades are the stepping stone to your future. Even if you don't want to study science or maths further, the grades you get now will open doors in the future. Differentiation Part 1 https://youtu.be/KlbNTcIlct
From playlist A-Level Maths | Revision Playlist
"I need a better description": An Investigation Into User Expectations For Differential Privacy
A Google TechTalk, presented by Rachel Cummings, 2021/03/12 ABSTRACT: Differential Privacy for ML Series. Despite recent widespread deployment of differential privacy, relatively little is known about what users think of differential privacy. In this work, we seek to explore users' privac
From playlist Differential Privacy for ML
Pre-recorded lecture 2: Nijenhuis torsion and its basic properties
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Lecture 6: Exterior Derivative (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Daniel Robertz, University of Plymouth, (in collaboration with V. P. Gerdt, Dubna, Russia). Algorithmic Approach to Strong Consistency Analysis of Finite Difference Approximations to PDE Systems. Kolchin Seminar at Graduate Center CUNY, September 13, 2019
From playlist Fall 2019 Kolchin Seminar in Differential Algebra
Differentially Private Algorithms: Some Primitives and Paradigms - Kunal Talwar
Differential Privacy Symposium: Four Facets of Differential Privacy Saturday, November 12, 2016 https://www.ias.edu/differential-privacy More videos on http://video.ias.edu
From playlist Differential Privacy Symposium - November 12, 2016
Asymptotic valued differential fields
From playlist Spring 2019 Kolchin Seminar
Product Rule | Differentiation | Revision for Maths A-Level and IB
I want to help you achieve the grades you (and I) know you are capable of; these grades are the stepping stone to your future. Even if you don't want to study science or maths further, the grades you get now will open doors in the future. Tutoring - We can match you with an experienced t
From playlist A-Level Maths | Revision Playlist
Ex 1: Initial Value Problem - Separation of Variables
This video provides an example of how to solve an initial value problem that requires the technique of separation of variables. Video Library: http://mathispower4u.com Search by Topic: http://mathispower4u.wordpress.com
From playlist First Order Differential Equations: Separation of Variables
Jacob Leygonie (6/1/20): Differential calculus on persistence barcodes
Title: Differential calculus on persistence barcodes Abstract: We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the proposed framework uses lifts to the space of ordered barcodes, from which deri
From playlist ATMCS/AATRN 2020