Differential structures | Smooth functions | Real analysis | Algebraic geometry | Differential calculus
In mathematics, especially real analysis, a flat function is a smooth function all of whose derivatives vanish at a given point . The flat functions are, in some sense, the antitheses of the analytic functions. An analytic function is given by a convergent power series close to some point : In the case of a flat function we see that all derivatives vanish at , i.e. for all . This means that a meaningful Taylor series expansion in a neighbourhood of is impossible. In the language of Taylor's theorem, the non-constant part of the function always lies in the remainder for all . The function need not be flat at just one point. Trivially, constant functions on are flat everywhere. But there are also other, less trivial, examples. (Wikipedia).
What is a function? How do you use the vertical line test? Learn more about functions and determine if mappings, sets of ordered pairs, tables, or graphs are functions in this short algebra video. Need more math help? Check out our algebra and geometry lessons at katesmathlessons.com
From playlist Algebra 1
Reconsidering `functions' in modern mathematics | Arithmetic and Geometry Math Foundations 43
The general notion of `function' does not work in mathematics, just as the general notions of `number' or `sequence' don't work. This video explains the distinction between `closed' and `open' systems, and suggests that mathematical definitions should respect the open aspect of mathemat
From playlist Math Foundations
Using the vertical line test to determine if a graph is a function or not
👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Transcendental Functions 17 The Indefinite Integral of 1 over u du Example 1.mov
Example problems involving the integral of u to the power negative 1 du.
From playlist Transcendental Functions
Represent a Discrete Function Using Ordered Pairs, a Table, and Function Notation
This video explains how to represent a discrete function given as points as ordered pairs, a table, and using function notation. http://mathispower4u.com
From playlist Introduction to Functions: Function Basics
Transcendental Functions 17 The Indefinite Integral of 1 over u du Example 2.mov
More example problems involving the integral of 1 over u, du.
From playlist Transcendental Functions
(New Version Available) Inverse Functions
New Version: https://youtu.be/q6y0ToEhT1E Define an inverse function. Determine if a function as an inverse function. Determine inverse functions. http://mathispower4u.wordpress.com/
From playlist Exponential and Logarithmic Expressions and Equations
Describing Functions (Discrete Math)
This video covered the various ways to describe functions in a discrete math class.
From playlist Functions (Discrete Math)
What are bounded functions and how do you determine the boundness
👉 Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
R. Perales - Recent Intrinsic Flat Convergence Theorems
Given a closed and oriented manifold M and Riemannian tensors g0, g1, ... on M that satisfy g0 gj, vol(M, gj)→vol (M, g0) and diam(M, gj)≤D we will see that (M, gj) converges to (M, g0) in the intrinsic flat sense. We also generalize this to the non-empty bundary setting. We remark that u
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
R. Perales - Recent Intrinsic Flat Convergence Theorems (version temporaire)
Given a closed and oriented manifold M and Riemannian tensors g0, g1, ... on M that satisfy g0 gj, vol(M, gj)→vol (M, g0) and diam(M, gj)≤D we will see that (M, gj) converges to (M, g0) in the intrinsic flat sense. We also generalize this to the non-empty bundary setting. We remark that u
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry Part 1
At the start of the 20th century, David Hilbert asked which representations can arise by studying the monodromy of Fuchsian equations. This question was the starting point for a beautiful circle of ideas relating the topology of a complex algebraic variety X to the study of algebraic diffe
From playlist Felix Klein Lectures 2022
Strong coupling superconductivity and pseudogap in topological flat by Debanjan Chowdhury
DISCUSSION MEETING NOVEL PHASES OF QUANTUM MATTER ORGANIZERS: Adhip Agarwala, Sumilan Banerjee, Subhro Bhattacharjee, Abhishodh Prakash and Smitha Vishveshwara DATE: 23 December 2019 to 02 January 2020 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Recent theoretical and experimental
From playlist Novel Phases of Quantum Matter 2019
What is General Relativity? Lesson 41: The Commutator in Flat Space
What is General Relativity? Lesson 41: The Commutator in Flat Space We dig into the concept of the commutator of vector fields in order to prepare ourselves to appreciate the nature of the curvature tensor. Please consider supporting this channel via Patreon: https://www.patreon.com/XYL
From playlist What is General Relativity?
Exact rate of Nesterov Scheme - Dossal - Workshop 1 - CEB T1 2019
Dossal (INSA Toulouse) / 06.02.2019 Exact rate of Nesterov Scheme In 1984 Nesterov proposed an inertial gradient scheme to minimize convex functions which ensures a $1/n^2$ decay rate. In this talk, we give the exact decay rate of this scheme depending on the geometrical properties of t
From playlist 2019 - T1 - The Mathematics of Imaging
Bourbaki - 05/11/2016 - 1/4 - Piotr CHRUĹšCIEL
Piotr CHRUŚCIEL - Anti-gravité à la Carlotto et Schoen Les équations d’Einstein sont, dans leur nature, hyperboliques. Leurs solutions peuvent donc être construites en développant dans le temps des données initiales. Une des difficultés de la théorie est que ces données initiales ne sont
From playlist Bourbaki - 05 novembre 2016
Asghar Ghorbanpour: Scalar curvature of functional metrics on noncommutative tori
Talk by Asghar Ghorbanpour in Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/scalar-curvature-of-functional-metrics-on-noncommutative-tori/ on March 12, 2021
From playlist Global Noncommutative Geometry Seminar (Americas)
Tom Goldstein: "An empirical look at generalization in neural nets"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop II: PDE and Inverse Problem Methods in Machine Learning "An empirical look at generalization in neural nets" Tom Goldstein - University of Maryland Abstract: Generalization in neural nets is a mysterious phenomenon that has been studied
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Just because the tangent plane to a multivariable function is flat, it doesn't mean that point is a local minimum or a local maximum. There is a third possibility, new to multivariable calculus, called a "saddle point".
From playlist Multivariable calculus
This video explains what a mathematical function is and how it defines a relationship between two sets, the domain and the range. It also introduces three important categories of function: injective, surjective and bijective.
From playlist Foundational Math