Lambda calculus

Higher-order function

In mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following: * takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure), * returns a function as its result. All other functions are first-order functions. In mathematics higher-order functions are also termed operators or functionals. The differential operator in calculus is a common example, since it maps a function to its derivative, also a function. Higher-order functions should not be confused with other uses of the word "functor" throughout mathematics, see Functor (disambiguation). In the untyped lambda calculus, all functions are higher-order; in a typed lambda calculus, from which most functional programming languages are derived, higher-order functions that take one function as argument are values with types of the form . (Wikipedia).

Video thumbnail

Ex 1: Determine Higher Order Derivatives

This video provides an example of how to determine the first, second, third, and fourth derivative of a function. Complete Video List at http://www.mathispower4u.com

From playlist Higher Order Differentiation

Video thumbnail

Higher Order Derivatives of Trigonometric Functions

The video explains how to determine higher order derivatives of trigonometric functions. http://mathispower4u.wordpress.com/

From playlist Differentiation

Video thumbnail

Ex 2: Determine Higher Order Derivatives

This video provides an example of how to determine the first, second, and third derivative of a function. Complete Video List at http://www.mathispower4u.com

From playlist Higher Order Differentiation

Video thumbnail

Higher-Order Derivatives: Part 1 of 2

http://mathispower4u.wordpress.com/

From playlist Higher Order Differentiation

Video thumbnail

Lecture: Approximation 2018-09-10

Approximating higher order transfer functions. Taylor series, Padé approximants and response-based approximation.

From playlist Lectures

Video thumbnail

Ex: Higher Order Derivatives Using the Product Rule

This video explains how to find the first, second, and third derivative of a function that requires the product rule and chain rule. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Higher Order Differentiation

Video thumbnail

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

Video thumbnail

Determine if Ordered Pairs Represent a Function and Describe Behavior

This video explains how to determine is a relation given as a set of ordreed pairs is a function and if the function is increasing, decreasing, or constant. http://mathispower4u.com

From playlist Introduction to Functions: Function Basics

Video thumbnail

Working with Functions (1 of 2: Notation & Terminology)

More resources available at www.misterwootube.com

From playlist Working with Functions

Video thumbnail

Kotlin Functions Tutorial | Kotlin Functional Programming Explained | Kotlin Tutorial | Simplilearn

🔥Post Graduate Program In Full Stack Web Development: https://www.simplilearn.com/pgp-full-stack-web-development-certification-training-course?utm_campaign=KotlinFunctionsTutorial-obN78NEd47g&utm_medium=DescriptionFF&utm_source=youtube 🔥Caltech Coding Bootcamp (US Only): https://www.simpli

From playlist C++ Tutorial Videos

Video thumbnail

16.5: Higher Order Functions in JavaScript - Topics of JavaScript/ES6

In this video, I discuss "higher order functions" in JavaScript. 🎥 Next Video: https://youtu.be/EnYlhbpzhU4 🎥 Topics of JavaScript/ES6: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6YgpA3Oht-7B4NBQwFVe3pr 🎥 ES6 Arrow Function: https://youtu.be/mrYMzpbFz18 🎥 Closures in JavaScript: ht

From playlist Array Functions in JavaScript

Video thumbnail

Live Stream #121: map() and reduce() in JavaScript

In this live stream, I cover higher order functions in JavaScript and discuss them in the context of arrays: map() and reduce() 19:04 - Introduction to higher order functions 44:00 - map() 1:09:53 - reduce() 🔗 Arrays on MDN: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Referen

From playlist Live Stream Archive

Video thumbnail

Semantic models for higher-order Bayesian inference - Sam Staton, University of Oxford

In this talk I will discuss probabilistic programming as a method of Bayesian modelling and inference, with a focus on fully featured probabilistic programming languages with higher order functions, soft constraints, and continuous distributions. These languages are pushing the limits of e

From playlist Logic and learning workshop

Video thumbnail

Sarah Post: Rational extensions of superintegrable systems, exceptional polynomials & Painleve eq.s

Abstract: In this talk, I will discuss recent work with Ian Marquette and Lisa Ritter on superintegable extensions of a Smorodinsky Winternitz potential associated with exception orthogonal polynomials (EOPs). EOPs are families of orthogonal polynomials that generalize the classical ones b

From playlist Integrable Systems 9th Workshop

Video thumbnail

Galaxy bias and its implications for forward models (...) - F. Schmidt - Workshop 1 - CEB T3 2018

Fabian Schmidt (MPA) / 21.09.2018 Galaxy bias and its implications for forward models of the large-scale structure ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/

From playlist 2018 - T3 - Analytics, Inference, and Computation in Cosmology

Video thumbnail

ME564 Lecture 3: Taylor series and solutions to first and second order linear ODEs

ME564 Lecture 3 Engineering Mathematics at the University of Washington Taylor series and solutions to first and second order linear ODEs Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L03.pdf Matlab code: http://faculty.washington.edu/sbrunton/me564/matlab/L03_TaylorSeries.m C

From playlist Engineering Mathematics (UW ME564 and ME565)

Video thumbnail

Séverin Charbonnier: Topological recursion for fully simple maps

Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: Fully simple maps show strong relations with symplectic invariance of topological recursion and free probabilities. While ordinary maps satisfy topological recursion

From playlist Noncommutative geometry meets topological recursion 2021

Video thumbnail

Terence Tao: The circle method from the perspective of higher order Fourier analysis

Higher order Fourier analysis is a collection of results and methods that can be used to control multilinear averages (such as counts for the number of four-term progressions in a set) that are out of reach of conventional linear Fourier analysis methods (i.e., out of reach of the circle m

From playlist Harmonic Analysis and Analytic Number Theory

Video thumbnail

How to determine if an ordered pair 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

Related pages

Differential operator | First-class function | Derivative | Typed lambda calculus | Currying | Functional (mathematics) | Lambda calculus | Montague grammar | Operator (mathematics) | Apply | Anonymous function | Mathematics | Type system | Function (mathematics) | Kappa calculus | Tree traversal | Qsort | Integral | Calculus | Fold (higher-order function) | Record (computer science) | Combinatory logic | Object (computer science)