Complex analysis | Types of functions
In mathematics, antiholomorphic functions (also called antianalytic functions) are a family of functions closely related to but distinct from holomorphic functions. A function of the complex variable z defined on an open set in the complex plane is said to be antiholomorphic if its derivative with respect to z exists in the neighbourhood of each and every point in that set, where z is the complex conjugate. A definition of antiholomorphic function follows: "[a] function of one or more complex variables [is said to be anti-holomorphic if (and only if) it] is the complex conjugate of a holomorphic function ." One can show that if f(z) is a holomorphic function on an open set D, then f(z) is an antiholomorphic function on D, where D is the reflection against the x-axis of D, or in other words, D is the set of complex conjugates of elements of D. Moreover, any antiholomorphic function can be obtained in this manner from a holomorphic function. This implies that a function is antiholomorphic if and only if it can be expanded in a power series in z in a neighborhood of each point in its domain. Also, a function f(z) is antiholomorphic on an open set D if and only if the function f(z) is holomorphic on D. If a function is both holomorphic and antiholomorphic, then it is constant on any connected component of its domain. (Wikipedia).
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
Quantization by Branes and Geometric Langlands (Lecture 4) by Edward Witten
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 Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Sabyasachi Mukherjee: Interbreeding in conformal dynamics, and its applications near and far
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Celestial Amplitudes and Asymptotic Symmetries (Lecture 2) by Stephan Stieberger
PROGRAM RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online
From playlist Recent Developments in S-matrix Theory (Online)
Calculus 5.1a - Antiderivatives
An introduction to antiderivatives.
From playlist Calculus Chapter 5 (selected videos)
8ECM Plenary Lecture: Franc Forstnerič
From playlist 8ECM Plenary Lectures
Bhargav Bhatt - Prismatic cohomology and applications: Overview
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From playlist Minerva Lectures - Bhargav Bhatt
Ex 1: Antiderivative Concept - Given Information about f(x), Describe F(x)
This video explains how to describe the antiderivative function given information about f(x). Site: http://mathispower4u.com
From playlist The Antiderivative
Samson Shatashvili - 1/3 Supersymmetric Vacua and Integrability
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From playlist Samson Shatashvili - Supersymmetric Vacua and Integrability
Definition of an Injective Function and Sample Proof
We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil
From playlist Injective, Surjective, and Bijective Functions
The General Antiderivative of a Polynomial Function
This video explains how to find an antiderivative of a polynomial function.
From playlist The Antiderivative
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From playlist Calculus
Ex 2: Antiderivative Concept - Given Information about f(x), Describe F(x)
This video explains how to describe the antiderivative function given information about f(x). Site: http://mathispower4u.com
From playlist The Antiderivative
Lilya Budaghyan : On APN and AB power functions
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Kotlin Functions Tutorial | Kotlin Functional Programming Explained | Kotlin Tutorial | Simplilearn
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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
[Calculus] Antiderivatives || Lecture 41
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From playlist Calculus 1