Real numbers | Mathematical analysis | Multivariable calculus
In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers , or a subset of that contains an interval of positive length. Most real functions that are considered and studied are differentiable in some interval.The most widely considered such functions are the real functions, which are the real-valued functions of a real variable, that is, the functions of a real variable whose codomain is the set of real numbers. Nevertheless, the codomain of a function of a real variable may be any set. However, it is often assumed to have a structure of -vector space over the reals. That is, the codomain may be a Euclidean space, a coordinate vector, the set of matrices of real numbers of a given size, or an -algebra, such as the complex numbers or the quaternions. The structure -vector space of the codomain induces a structure of -vector space on the functions. If the codomain has a structure of -algebra, the same is true for the functions. The image of a function of a real variable is a curve in the codomain. In this context, a function that defines curve is called a parametric equation of the curve. When the codomain of a function of a real variable is a finite-dimensional vector space, the function may be viewed as a sequence of real functions. This is often used in applications. (Wikipedia).
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
Intro to Real Functions (3 of 4: Characteristics of a function)
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From playlist Working with Functions
Functions of equations - IS IT A FUNCTION
👉 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 Relation is a Function
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From playlist Intro to Functions
In this video we cover some rational function fundamentals, including asymptotes and interecepts.
From playlist Polynomial Functions
Determining if a function is a polynomial or not then determine degree and LC
👉 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?
Domain of a simple rational function in interval and set notation
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain of a rational function, we first find the values of x
From playlist Domain of a function with a fraction | Linear
Learn how to identify if a function is a polynomial and identify the degree and LC
👉 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?
Determine if the equation represents a function
👉 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
Worldwide Calculus: Multivariable Functions
Lecture on 'Multivariable Functions' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Multivariable Calculus
Complex analysis: Holomorphic functions
This lecture is part of an online undergraduate course on complex analysis. We define holomorphic (complex differentiable) functions, and discuss their basic properties, in particular the Cauchy-Riemann equations. For the other lectures in the course see https://www.youtube.com/playlist
From playlist Complex analysis
Part I: Complex Variables, Lec 2: Functions of a Complex Variable
Part I: Complex Variables, Lecture 2: Functions of a Complex Variable Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 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: Calculus of Complex Variables
Part I: Complex Variables, Lec 3: Conformal Mappings
Part I: Complex Variables, Lecture 3: Conformal Mappings Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 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: Calculus of Complex Variables
Part I: Complex Variables, Lec 5: Integrating Complex Functions
Part I: Complex Variables, Lecture 5: Integrating Complex Functions Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 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: Calculus of Complex Variables
Complex Analysis L01: Overview & Motivation, Complex Arithmetic, Euler's Formula & Polar Coordinates
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From playlist Engineering Math: Crash Course in Complex Analysis
Intro to Jacobian + differentiability
A lecture that introduces the Jacobian matrix and its determinant. Such ideas may be thought of as a general derivative of a vector-valued function of many variables and find uses in integration theory.
From playlist Several Variable Calculus / Vector Calculus
Define a linear function. Determine if a linear function is increasing or decreasing. Interpret linear function models. Determine linear functions. Site: http://mathispower4u.com
From playlist Introduction to Functions: Function Basics