Functions and mappings | Mathematical relations
In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly X itself) to Y. The subset S, that is, the domain of f viewed as a function, is called the domain of definition of f. If S equals X, that is, if f is defined on every element in X, then f is said to be total. More technically, a partial function is a binary relation over two sets that associates every element of the first set to at most one element of the second set; it is thus a functional binary relation. It generalizes the concept of a (total) function by not requiring every element of the first set to be associated to exactly one element of the second set. A partial function is often used when its exact domain of definition is not known or difficult to specify. This is the case in calculus, where, for example, the quotient of two functions is a partial function whose domain of definition cannot contain the zeros of the denominator. For this reason, in calculus, and more generally in mathematical analysis, a partial function is generally called simply a function. In computability theory, a general recursive function is a partial function from the integers to the integers; for many of them no algorithm can exist for deciding whether they are in fact total. When arrow notation is used for functions, a partial function from to is sometimes written as or However, there is no general convention, and the latter notation is more commonly used for inclusion maps or embeddings. Specifically, for a partial function and any one has either: * (it is a single element in Y), or * is undefined. For example, if is the square root function restricted to the integers defined by: if, and only if, then is only defined if is a perfect square (that is, ). So but is undefined. (Wikipedia).
What are bounded functions and how do you determine the boundness
π Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
When is a function bounded below?
π Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
This video explains what a mathematical function is and how it defines a relationship between two sets, the domain and the range. It also introduces three important categories of function: injective, surjective and bijective.
From playlist Foundational Math
Absolute or relative minimum of graph?
π Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
π Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
π Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
π Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
π Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
Pre-Calculus - Vocabulary of functions
This video describes some of the vocabulary used with functions. Specifically it covers what a function is as well as the basic idea behind its domain and range. For more videos visit http://www.mysecretmathtutor.com
From playlist Pre-Calculus - Functions
Complex Analysis L07: Analytic Functions Solve Laplace's Equation
This video shows that the real and imaginary parts of analytic complex functions solve Laplace's equation. These are known as harmonic functions. @eigensteve on Twitter eigensteve.com databookuw.com
From playlist Engineering Math: Crash Course in Complex Analysis
Partial derivatives - How to solve?
βΊ My Partial Derivatives course: https://www.kristakingmath.com/partial-derivatives-course Partial derivatives are just like regular derivatives, but for multivariable functions. Weβre used to taking the derivative of a single variable function, which is simple because we just take the de
From playlist Calculus III
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 are Exact Differential Equations (Differential Equations 28)
https://www.patreon.com/ProfessorLeonard An explanation of the origin, use, and solving of Exact Differential Equations
From playlist Differential Equations
ME565 Lecture 3: Integration in the complex plane (Cauchy-Goursat Integral Theorem)
ME565 Lecture 3 Engineering Mathematics at the University of Washington Integration in the complex plane (Cauchy-Goursat Integral Theorem) Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L03.pdf Course Website: http://faculty.washington.edu/sbrunton/me565/ http://faculty.wash
From playlist Engineering Mathematics (UW ME564 and ME565)
Worldwide Calculus: Differentiation Rules
Lecture on 'Differentiation Rules' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Derivatives
Part III: Partial Derivatives, Lec 4 | MIT Calculus Revisited: Multivariable Calculus
Part III: Partial Derivatives, Lecture 4: The Chain Rule Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-007F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Calculus Revisited: Multivariable Calculus
Worldwide Calculus: Implicit Differentiation- Multivariable Calculus
Lecture on 'Implicit Differentiation- Multivariable Calculus' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Derivatives
Worldwide Calculus: Change of Coordinates
Lecture on 'Change of Coordinates' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Derivatives
Overview of one to one functions
π Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
PHYS 146 Waves part 2: The Wave Equation
Video lecture for PHYS 146 at the University of Alberta. Shows the derivation of the wave equation from first principles.
From playlist UAlberta: PHYS 146 - Fluids and Waves with Roger Moore | CosmoLearning.org Physics