In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations. However, a more restricted meaning is often used, where a functional equation is an equation that relates several values of the same function. For example, the logarithm functions are essentially characterized by the logarithmic functional equation If the domain of the unknown function is supposed to be the natural numbers, the function is generally viewed as a sequence, and, in this case, a functional equation (in the narrower meaning) is called a recurrence relation. Thus the term functional equation is used mainly for real functions and complex functions. Moreover a smoothness condition is often assumed for the solutions, since without such a condition, most functional equations have very irregular solutions. For example, the gamma function is a function that satisfies the functional equation and the initial value There are many functions that satisfy these conditions, but the gamma function is the unique one that is meromorphic in the whole complex plane, and logarithmically convex for x real and positive (Bohr–Mollerup theorem). (Wikipedia).
A first example problem solving a linear, second-order, homogeneous, ODE with variable coefficients around a regular singular point.
From playlist Differential Equations
B25 Example problem solving for a Bernoulli equation
See how to solve a Bernoulli equation.
From playlist Differential Equations
B12 Example problem with a linear equation
Solving an example problem for a linear equation.
From playlist Differential Equations
B13 Example problem with a linear equation
Solving an example problem for a linear equation.
From playlist Differential Equations
B10 Example problem with a linear equation
Solving a linear equation.
From playlist Differential Equations
B11 Example problem with a linear equation
Solving an example problem for a linear equation.
From playlist Differential Equations
Determine if the Functions are Linearly Independent or Linearly Dependent
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to determine if three functions are linearly independent or linearly dependent using the definition.
From playlist Differential Equations
Introduction to Parametric Equations
This video defines a parametric equations and shows how to graph a parametric equation by hand. http://mathispower4u.yolasite.com/
From playlist Parametric Equations
Learn how to eliminate the parameter with trig functions
Learn how to eliminate the parameter in a parametric equation. A parametric equation is a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters. Eliminating the parameter allows us to write parametric equation in r
From playlist Parametric Equations
What is the Schrödinger Equation? A basic introduction to Quantum Mechanics
This video provides a basic introduction to the Schrödinger equation by exploring how it can be used to perform simple quantum mechanical calculations. After explaining the basic structure of the equation, the infinite square well potential is used as a case study. The separation of variab
From playlist Quantum Physics
Separation of variables and the Schrodinger equation
A brief explanation of separation of variables, application to the time-dependent Schrodinger equation, and the solution to the time part. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/
From playlist Mathematical Physics II - Youtube
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
Guy Casale, University of Rennes
March 26, Guy Casale, University of Rennes Algebraic solutions to Kummer differential equation
From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra
Title: Algebraic Independence of Functions Satisfying Nonlinear Polynomial Mahler Equations
From playlist Differential Algebra and Related Topics VII (2016)
Calculus AB Homework Day 1 - Review 1: Functions
Download Packet: https://goo.gl/aCcjPn ================================= AP Calculus AB / IB Math SL Review 1: Functions =================================
From playlist AP Calculus AB
Lucia Di Vizio : Méthodes galoisiennes appliquées aux équations fonctionnelles issues de la...
CONFERENCE Recording during the thematic meeting : « ALEA Days» the March 16, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathemat
From playlist Combinatorics
Ordinary Differential Equations and Applications by A. K. Nandakumaran,P. S. Datti & Raju K. George,Department of Mathematics,IISc Bangalore.For more details on NPTEL visit http://nptel.ac.in.
From playlist IISc Bangalore: Ordinary Differential Equations and Applications | CosmoLearning.org Mathematics
How to solve differentiable equations with logarithms
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations