In mathematics a P-recursive equation can be solved for polynomial solutions. Sergei A. Abramov in 1989 and Marko Petkovšek in 1992 described an algorithm which finds all polynomial solutions of those recurrence equations with polynomial coefficients. The algorithm computes a degree bound for the solution in a first step. In a second step an ansatz for a polynomial of this degree is used and the unknown coefficients are computed by a system of linear equations. This article describes this algorithm. In 1995 Abramov, Bronstein and Petkovšek showed that the polynomial case can be solved more efficiently by considering power series solution of the recurrence equation in a specific power basis (i.e. not the ordinary basis ). Other algorithms which compute rational or hypergeometric solutions of a linear recurrence equation with polynomial coefficients also use algorithms which compute polynomial solutions. (Wikipedia).
C07 Homogeneous linear differential equations with constant coefficients
An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.
From playlist Differential Equations
How to solve a system of equations with infinite many solutions
👉Learn how to solve a system of equations by substitution. To solve a system of equations means to obtain a common values of the variables that makes the each of the equation in the system true. To solve a system of equations by substitution, we solve for one of the variables in one of the
From playlist Solve a System Algebraically | Algebra 2
Differential Equations | Second order linear homogeneous equations with repeated roots.
We derive the general solution to a second order linear homogeneous differential equation with constant coefficients whose companion polynomial has a repeated root.
From playlist Linear Differential Equations
Solving Polynomial Equations Graphically
http://mathispower4u.wordpress.com/
From playlist Solving Polynomial Equations / Increasing and Decreasing Polynomials
Totient and Factoring - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Differential Equations | Frobenius' Method part 2
From Garden of the Gods in Colorado Springs, we present a Theorem regarding Frobenius Series solutions to a certain family of second order homogeneous differential equations. An example is also explored. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Series Solutions for Differential Equations
Differential Equations | Frobenius' Method: Example 2
We give an example of solving a second order differential equations using Frobenius' method. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Series Solutions for Differential Equations
Sergey Yurkevich - How to Conjecture and Prove that the Generating Function of the Yang-Zagier (...)
In a recent paper Don Zagier mentions a mysterious integer sequence $(a_{n})_{n\geq0}$ which arises from a solution of a topological ODE discovered by Marco Bertola, Boris Dubrovin and Di Yang. In my talk I show how to conjecture, prove and even quantify that $(a_{n})_{n\geq0}$ actually ad
From playlist Combinatorics and Arithmetic for Physics: special days
Solving a system of equation with infinite solutions using substitution
👉Learn how to solve a system of equations by substitution. To solve a system of equations means to obtain a common values of the variables that makes the each of the equation in the system true. To solve a system of equations by substitution, we solve for one of the variables in one of the
From playlist Solve a System Algebraically | Algebra 2
Bertrand Eynard - Considerations about Resurgence Properties of Topological Recursion
To a spectral curve $S$ (e.g. a plane curve with some extra structure), topological recursion associates a sequence of invariants: some numbers $F_g(S)$ and some $n$-forms $W_{g,n}(S)$. First we show that $F_g(S)$ grow at most factorially at large $g$, $F_g = O((
From playlist Resurgence in Mathematics and Physics
Is it a polynomial with two variables
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever?
In this video, we take a look at one of the most beautiful algorithms ever created: the Fast Fourier Transform (FFT). This is a tricky algorithm to understand so we take a look at it in a context that we are all familiar with: polynomial multiplication. You will see how the core ideas of t
From playlist Fourier
Differential Equations: 2nd Order Non-Homogeneous Linear Differential Equations
How to solve 2nd order linear differential equations when the F(t) term is non-zero.
From playlist Basics: Differential Equations
Cutting Planes Proofs of Tseitin and Random Formulas - Noah Fleming
Computer Science/Discrete Mathematics Seminar II Topic: Cutting Planes Proofs of Tseitin and Random Formulas Speaker: Noah Fleming Affiliation: University of Toronto Date: May 5, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Alexandra SHLAPENTOKH - Defining Valuation Rings and Other Definability Problems in Number Theory
We discuss questions concerning first-order and existential definability over number fields and function fields in the language of rings and its extensions. In particular, we consider the problem of defining valuations rings over finite and infinite algebraic extensions
From playlist Mathematics is a long conversation: a celebration of Barry Mazur
Particular solution of an ode: polynomial
Illustrates how to find a particular solution of an inhomogeneous, second-order, constant-coefficient ode when the inhomogeneous term is a polynomial. Book at http://bookboon.com/en/differential-equations-with-youtube-examples-ebook
From playlist Differential Equations with YouTube Examples
Differential Equations | Frobenius' Method -- Example 1
From the desert, we present an example of a Frobenius series solution to a second order homogeneous differential equation. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Series Solutions for Differential Equations
Chair's Talk -- Conjectures (Vladimir Matveev) & Zoom Talk (Andrey Konyaev): Monday 14 February
SMRI -MATRIX Symposium: Nijenhuis Geometry and Integrable Systems Week 2 (MATRIX),14 February 2022 0:00:00 Chair's Talk -- Conjectures, Vladimir Matveev 0:50:55 Zoom Talk, Andrey Konyaev 1:32:58 Questions from the Audience ----------------------------------------------------------------
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
Yvain BRUNED - Bogoliubov Type Recursions for Renormalisation in Regularity Structures
Hairer's regularity structures transformed the solution theory of singular stochastic partial differential equations. The notions of positive and negative renormalisation are central and the intricate interplay between these two renormalisation procedures is captured through the combinatio
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Classify a polynomial then determining if it is a polynomial or not
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?