In mathematics, a functional (as a noun) is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author). * In linear algebra, it is synonymous with linear forms, which are linear mapping from a vector space into its field of scalars (that is, an element of the dual space ) * In functional analysis and related fields, it refers more generally to a mapping from a space into the field of real or complex numbers. In functional analysis, the term linear functional is a synonym of linear form; that is, it is a scalar-valued linear map. Depending on the author, such mappings may or may not be assumed to be linear, or to be defined on the whole space * In computer science, it is synonymous with higher-order functions, that is, functions that take functions as arguments or return them. This article is mainly concerned with the second concept, which arose in the early 18th century as part of the calculus of variations. The first concept, which is more modern and abstract, is discussed in detail in a separate article, under the name linear form. The third concept is detailed in the computer science article on higher-order functions. In the case where the space is a space of functions, the functional is a "function of a function", and some older authors actually define the term "functional" to mean "function of a function".However, the fact that is a space of functions is not mathematically essential, so this older definition is no longer prevalent. The term originates from the calculus of variations, where one searches for a function that minimizes (or maximizes) a given functional. A particularly important application in physics is search for a state of a system that minimizes (or maximizes) the action, or in other words the time integral of the Lagrangian. (Wikipedia).
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
In this video, I talk about the definition of a function and properties of functions. I also go over some examples of how to determine whether a relation is a function or not and how to evaluate functions. Enjoy! Facebook: https://www.facebook.com/braingainzofficial Instagram: https://
From playlist College Algebra
As part of the college algebra series, this Center of Math video will teach you the basics of functions, including how they're written and what they do.
From playlist Basics: College Algebra
What is Functional Programming?
We will discuss the state of functional programming in brief across several languages. Also a discussion on the broader goals of functional programming and this meetup. EVENT: OKC FP 2020 SPEAKER: Scott Murphy PUBLICATION PERMISSIONS: The conference organizer provided Coding Tech wit
From playlist Functional Programming
Programming Languages - (part 5 of 7)
How source code becomes a running program, how languages are categorized, and a survey of important languages. Part of a larger series teaching programming. Visit http://codeschool.org
From playlist Programming Languages
The Essence of Functional Programming
This talk dives into the origins of functional programming, going all the way back to where the term was first introduced, to see how it evolved over time into our modern understanding of what FP essentially involves. PUBLICATION PERMISSIONS: Original video was published with the Creative
From playlist Functional Programming
What is a Function? Calculus for Beginners: Dr Chris Tisdell Live Stream
What is a function and how are they useful? This video will answer these questions from an elementary mathematics point of view. Functions are a bit like a machine that follows a processing rule. You input something (like a number), the machine processes the number according to the rule,
From playlist Calculus for Beginners
Working with Functions (1 of 2: Notation & Terminology)
More resources available at www.misterwootube.com
From playlist Working with Functions
Determine if the equation represents a function
👉 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
Lecture with Ole Christensen. Kapitler: 00:00 - Introduction; 06:45 - Vector Spaces; 07:15 - Example 1; 12:00 - Mathematical Tool - Fourier Transform; 17:00 - Example 2; 20:00 - Example 3; 23:00 - New Concept - Norm; 27:45 - Lemma 2.1.2 - The Opposite Triangle Inequality; 35:15 - Convergen
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
SHM - 16/01/15 - Constructivismes en mathématiques - Henri Lombardi
Henri Lombardi (LMB, Université de Franche-Comté), « Foundations of Constructive Analysis, Bishop, 1967 : une refondation des mathématiques, constructive, minimaliste et révolutionnaire »
From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques
In this presentation, you'll hear from University of Warsaw professors sharing their experience teaching an analysis course using Mathematica. The presenters give examples of problems where Mathematica can be used effectively as an aid in solving mathematical problems, or at least to inspi
From playlist Wolfram Technology Conference 2020
Mathematica Experts Live: Integration with R using RLink
Yu-Sung Chang gives an overview of Mathematica's built-in integration with R using RLink as part of Mathematica Experts Live: New in Mathematica 9. For more information about Mathematica, please visit: http://www.wolfram.com/mathematica
From playlist Mathematica Experts Live: New in Mathematica 9
The big mathematics divide: between "exact" and "approximate" | Sociology and Pure Maths | NJW
Modern pure mathematics suffers from a major schism that largely goes unacknowledged: that many aspects of the subject are parading as "exact theories" when in fact they are really only "approximate theories". In this sense they can be viewed either as belonging more properly to applied ma
From playlist Sociology and Pure Mathematics
Mathematical Functions and Properties
The Wolfram Language has over 250 mathematical functions, including well-known elementary and special functions that have played a crucial role in the development of science for decades. Although this set is almost complete, we are continuously implementing new functionality for mathematic
From playlist Wolfram Technology Conference 2020
What is a Function in Math and Physics? (A more intuitive explanation of Function Definition)
0:00 Introduction 3:35 Examples of functions and why we care 14:55 Make own function 19:12 Definition of a function 21:48 Outro
From playlist Summer of Math Exposition Youtube Videos
Determine whether an equation determines y as a functions of x
http://www.freemathvideos.com In this video series I show how we determine the difference between a relation and a function. A function is a relation where every input value maps to exactly one output value. Every function can be written in function notation. I am a math teacher that provi
From playlist What is the Domain and Range of the Function
In this presentation from the Wolfram Technology Conference, Todd Gayley provides an overview of the main connectivity tools in Mathematica and shares guidelines about deciding which one is right for any specific application. For more information about Mathematica, please visit: http://ww
From playlist Wolfram Technology Conference 2012