Meromorphic functions | Rational functions | Algebraic varieties | Morphisms of schemes

Rational function

In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K. In this case, one speaks of a rational function and a rational fraction over K. The values of the variables may be taken in any field L containing K. Then the domain of the function is the set of the values of the variables for which the denominator is not zero, and the codomain is L. The set of rational functions over a field K is a field, the field of fractions of the ring of the polynomial functions over K. (Wikipedia).

Rational function
Video thumbnail

2.11117 What is a rational function Functions

http://www.freemathvideos.com presents: Learn math your way. My mission is to provide quality math education to everyone that is willing to receive it. This video is only a portion of a video course I have created as a math teacher. Please visit my website to join my mailing list, downloa

From playlist Rational Functions - Understanding

Video thumbnail

Rational Functions

In this video we cover some rational function fundamentals, including asymptotes and interecepts.

From playlist Polynomial Functions

Video thumbnail

Math 023 Fall 2022 102422 Rational Functions part I

("Morally speaking....") Approximation of the behavior of polynomials near zeroes: what's really going on? (Crux: if A is basically A_0, and B is basically B_0, then their product is basically A_0 B_0.) Example. Rational functions: definition. Digression: definition of proper and impr

From playlist Course 1: Precalculus (Fall 2022)

Video thumbnail

Multiplication & Division of Functions (1 of 4: Intercepts & asymptotes)

More resources available at www.misterwootube.com

From playlist Further Work with Functions

Video thumbnail

Math 023 Precalculus Day 21: Rational Functions

Rational functions: definition, proper and improper rational functions; simplest example (1/x); observations; various examples; determining vertical and horizontal asymptotes

From playlist Course 1: Precalculus

Video thumbnail

Graph Rational Functions

http://mathispower4u.wordpress.com/

From playlist Graphing Rational Functions

Video thumbnail

Pre-Calculus - The vocabulary of rational functions

This video will cover some of the common terms mentioned when working with rational functions. Remember a rational function is formed from taking one polynomial and dividing it by another polynomial. For more videos please visit http://www.mysecretmathtutor.com

From playlist Pre-Calculus

Video thumbnail

Determining Vertical and Horizontal Asymptotes of Rational Functions

This video explains how to determine horizontal and vertical asymptotes of a rational function, not using limits. It is appropriate for an algebra class. http://mathispower4u.yolasite.com/

From playlist Rational Expressions and Equations

Video thumbnail

algebraic geometry 31 Rational maps

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of rational functions and rational maps, and gives an example of a cubic curve that is not birational to the affine line.

From playlist Algebraic geometry I: Varieties

Video thumbnail

Kelly Bickel: Singular rational inner functions on the polydisk

This talk will discuss how to study singular rational inner functions (RIFs) using their zero set behaviors. In the two-variable setting, zero sets can be used to define a quantity called contact order, which helps quantify derivative integrability and non-tangential regularity. In the

From playlist Analysis and its Applications

Video thumbnail

Christoph Koutschan

Diagonals of Rational Functions Diagonals of rational functions naturally occur in many applications, study several families of rational functions in three or four variables and investigate the nature of their diagonals (hypergeometric 2F1 functions, Heun functions, modular forms, functi

From playlist DART X

Video thumbnail

George Labahn 3/10/16 Part 1

Symbolic-Numeric Computation with Rational Functions Symbolic-Numeric Computing Seminar

From playlist Symbolic-Numeric Computing Seminar

Video thumbnail

Random Matrices and Their Limits - R. Speicher - Workshop 2 - CEB T3 2017

Roland Speicher / 26.10.17 Random Matrices and Their Limits The free probability perspective on random matrices is that the large size limit of random matrices is given by some (usually interesting) operators on Hilbert spaces and corresponding operator algebras. The prototypical example

From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

Video thumbnail

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?

Video thumbnail

The strangest function I know (linear but not continuous?? huh??)

Keep exploring at https://brilliant.org/TreforBazett. Get started for free, and hurry—the first 200 people get 20% off an annual premium subscription. When you think of linear functions from R to R, you are probably thinking about lines. However, I'm going to show you in this video a craz

From playlist Cool Math Series

Video thumbnail

Master How to determine the domain of a rational function

Subscribe! http://www.freemathvideos.com Want more math video lessons? Visit my website to view all of my math videos organized by course, chapter and section. The purpose of posting my free video tutorials is to not only help students but allow teachers the resources to flip their classro

From playlist Rational Functions #Master

Video thumbnail

Manjul Bhargava: What is the Birch-Swinnerton-Dyer Conjecture, and what is known about it?

Abstract: The Birch and Swinnerton-Dyer Conjecture has become one of the central problems of number theory and represents an important next frontier. The purpose of this lecture is to explain the problem in elementary terms, and to describe the implications of Andrew Wiles' groundbreaking

From playlist Abel Lectures

Related pages

Field of fractions | Signal processing | Zero function | Z-transform | Complex analysis | Julia set | Algebraic fraction | Coefficient | Clearing denominators | Codomain | Fraction | Interpolation | Riemann sphere | Function field of an algebraic variety | Polynomial | Linear time-invariant system | Domain of a function | Irreducible fraction | Geometric series | Point at infinity | Infinite impulse response | Rational number | Like terms | Imaginary unit | Polynomial ring | Approximation | Degree of a polynomial | Impulse response | Laplace transform | Asymptotic analysis | Variable (mathematics) | Meromorphic function | Polynomial function | Projective line | Equivalence class | Value (mathematics) | Monic polynomial | Mathematics | Degree of an algebraic variety | Function (mathematics) | Field (mathematics) | Recurrence relation | Removable singularity | Real number | Partial fraction decomposition | Constant term | Ring (mathematics) | Constant function | Taylor series | Möbius transformation | Network synthesis | Numerical analysis | Abstract algebra | Complex number | Polynomial greatest common divisor | Unique factorization domain | Computer algebra system