In mathematics, a square-integrable function, also called a quadratically integrable function or function or square-summable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite. Thus, square-integrability on the real line is defined as follows. One may also speak of quadratic integrability over bounded intervals such as for . An equivalent definition is to say that the square of the function itself (rather than of its absolute value) is Lebesgue integrable. For this to be true, the integrals of the positive and negative portions of the real part must both be finite, as well as those for the imaginary part. The vector space of square integrable functions (with respect to Lebesgue measure) forms the Lp space with . Among the Lp spaces, the class of square integrable functions is unique in being compatible with an inner product, which allows notions like angle and orthogonality to be defined. Along with this inner product, the square integrable functions form a Hilbert space, since all of the Lp spaces are complete under their respective p-norms. Often the term is used not to refer to a specific function, but to equivalence classes of functions that are equal almost everywhere. (Wikipedia).
(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
Math 023 Fall 2022 113022 Inverse Trigonometric Functions
Recall: what functions are invertible? Functions that pass the "horizontal line test" - that is, one-to-one functions. Is the sine function invertible? No. But if we restrict it to, say [-pi/2, pi/2], then it is invertible. So we define the inverse sine function to be the inverse of t
From playlist Course 1: Precalculus (Fall 2022)
Math 023 Precalculus Day 16: Linear and Quadratic Functions
Linear functions: definition, examples (linear depreciation, cost function, marginal cost, comment about rate of change, velocity). Quadratic functions: using completing the square to simplify the expression; finding the vertex, axis of symmetry, etc.
From playlist Course 1: Precalculus
Calculus 1.5 Inverse Functions and Logarithms
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Math 030 Calculus I 031315: Inverse Functions and Differentiation
Inverse functions. Examples of determining the inverse. Relation between the graphs of a function and its inverse. One-to-one functions. Restricting the domain of a function so that it is invertible. Differentiability of inverse functions; relation between derivatives of function and
From playlist Course 2: Calculus I
Graphing Squared Functions (2 of 2: Cubic + semi-circle examples)
More resources available at www.misterwootube.com
From playlist Further Work with Functions
Abstract Algebra | Injective Functions
We give the definition of an injective function, an outline of proving that a given function is injective, and a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
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
Completeness and Orthogonality
A discussion of the properties of Completeness and Orthogonality of special functions, such as Legendre Polynomials and Bessel functions.
From playlist Mathematical Physics II Uploads
Calculus 15.2 Double Integrals over General Regions
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Calculus 15.6 Triple Integrals
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
What is General Relativity? Lesson 35: Math Break: Integration/Radicals
What is General Relativity? Lesson 34: Math Break - Integration of Rational Functions involving the square root of a quadratic, This is another mathematics review to prepare for the introduction of elliptic integrals. The paper by Kostic I occasionally refer to during these lectures can
From playlist What is General Relativity?
Lec 29 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 29: Fourier series (part 2) License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008
Calculus 15.4 Applications of Double Integrals
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Mod-01 Lec-11 Integration II | Biomathematics by IIT Bombay
Biomathematics by Dr. Ranjith Padinhateeri, Department of Biotechnology, IIT Bombay.For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist IIT Bombay: Biomathematics | CosmoLearning.org Bioengineering
Calculus 2 - Full College Course
Learn Calculus 2 in this full college course. This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Check out her YouTube channel: https://www.youtube.com/channel/UCkyLJh6hQS1TlhUZxOMjTFw ⭐️ Prerequisites ⭐️ 🎥 Algebra: https://www.yout
From playlist Mathematics
Worldwide Calculus: Integration in R²
Lecture on 'Integration in R²' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Integrals
Area Between Curves #2 (OpenStax Calculus, Vol. 2, Section 2.1)
This video contains solutions to sample problems from OpenStax Calculus, Volume 2, Section 2.1: Area Between Curves. This is the second of two videos, focusing on more complicated examples. OpenStax Calculus Vol. 2: https://openstax.org/details/books/calculus-volume-2
From playlist Calculus II
Given a quadratic function, find the inverse and determine if a function or not
👉 Learn how to find the inverse of a quadratic function. A quadratic function is a function whose highest exponent in the variable(s) of the function is 2. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the inverse of
From playlist Find the Inverse of a Function
What is General Relativity? Lesson 34: Math Break - Integration of Rational Functions
What is General Relativity? Lesson 34: Math Break - Integration of Rational Functions This is another mathematics review to prepare for the introduction of elliptic integrals. The paper by Kostic I occasionally refer to during these lectures can be found here: https://arxiv.org/abs/1201
From playlist What is General Relativity?