Differential operators | Linear algebra | Types of functions
In mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the degree of homogeneity, or simply the degree; that is, if k is an integer, a function f of n variables is homogeneous of degree k if for every and For example, a homogeneous polynomial of degree k defines a homogeneous function of degree k. The above definition extends to functions whose domain and codomain are vector spaces over a field F: a function between two F-vector spaces is homogeneous of degree if for all nonzero and This definition is often further generalized to functions whose domain is not V, but a cone in V, that is, a subset C of V such that implies for every nonzero scalar s. In the case of functions of several real variables and real vector spaces, a slightly more general form of homogeneity called positive homogeneity is often considered, by requiring only that the above identities hold for and allowing any real number k as a degree of homogeneity. Every homogeneous real function is positively homogeneous. The converse is not true, but is locally true in the sense that (for integer degrees) the two kinds of homogeneity cannot be distinguished by considering the behavior of a function near a given point. A norm over a real vector space is an example of a positively homogeneous function that is not homogeneous. A special case is the absolute value of real numbers. The quotient of two homogeneous polynomials of the same degree gives an example of a homogeneous function of degree zero. This example is fundamental in the definition of projective schemes. (Wikipedia).
Determine if a Function is a Homogeneous Function
This video explains how to determine if a function is homogeneous and if it is homogeneous, what is the degree of the homogeneous function. Website: http://mathispower4u.com
From playlist First Order Homogeneous Differential Equations
Determine if the Function f(x, y) = x[ln(sqrt(x^2 + y^2) - ln(y)] + y*e^(x/y) Homogeneous?
In this video we have a function f(x, y) = x[ln(sqrt(x^2 + y^2) - ln(y)] + y*e^(x/y). We are asked to determine if it is homogeneous. Recall a function f(x, y) is homogeneous of degree n if f(lamda*x, lambda*y) = (lambda)^n * f(x, y). We apply this definition to the function in this proble
From playlist Homogeneous Differential Equations
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👉 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
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👉 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
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
Introduction to Homogeneous Differential Equations
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From playlist Differential Equations
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
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👉 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
Determine if a Function is a Polynomial Function
This video explains how to determine if a function is a polynomial function. http://mathispower4u.com
From playlist Determining the Characteristics of Polynomial Functions
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If you have a DE of the form Mdx + Ndy = 0, we say it is homogeneous if both M and N are homogeneous functions of the same degree. If we let y = ux or x = vy we can then transform this DE into a separable DE. In this video I explain why this actually happens. This video does not give an ac
From playlist Homogeneous Differential Equations
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In the previous video (https://youtu.be/3Kox-3APznI) we examined solving homogeneous linear ordinary differential equations (the forcing function was equal to 0). In this video we discuss how to solve nonhomogeneous linear ordinary differential equations which has the forcing function equ
From playlist Ordinary Differential Equations
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DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño
From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)
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From playlist Elementary Differential Equations
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From playlist Course 9: Basic Functional and Harmonic Analysis
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DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño
From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)
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DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño
From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)
Homogenization of a Quasilinear Elliptic Problem in a Two-Component Domain...by Rheadel Fulgencio
DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño
From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)
Determine if a First-Order Differential Equation is Homogeneous - Part 1
This video explains how to determine if a given linear first order differential equation is homogeneous using the ratio definition. Website: http://mathispower4u.com
From playlist First Order Homogeneous Differential Equations
Determine if a Relation is a Function
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From playlist Intro to Functions