Course Title:
... What does it mean to say a function is continuous at a point, over an interval and at an endpoint? What are the types of discontinuities? What does the Intermediate Value Theorem say? Skills check, ability to: Identify where a function is continuous given its graph or its algebraic equation Sketch f ...
... What does it mean to say a function is continuous at a point, over an interval and at an endpoint? What are the types of discontinuities? What does the Intermediate Value Theorem say? Skills check, ability to: Identify where a function is continuous given its graph or its algebraic equation Sketch f ...
Lecture 2: Entropy and mutual information
... Before we get to the proof, we have to introduce some preliminary concepts like Jensen’s inequality and the relative entropy. Jensen’s inequality tells us something about the expected value of a random variable after applying a convex function to it. We say function is convex on the interval [a, b] ...
... Before we get to the proof, we have to introduce some preliminary concepts like Jensen’s inequality and the relative entropy. Jensen’s inequality tells us something about the expected value of a random variable after applying a convex function to it. We say function is convex on the interval [a, b] ...
Function of several real variables
In mathematical analysis, and applications in geometry, applied mathematics, engineering, natural sciences, and economics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The ""input"" variables take real values, while the ""output"", also called the ""value of the function"", may be real or complex. However, the study of the complex valued functions may be easily reduced to the study of the real valued functions, by considering the real and imaginary parts of the complex function; therefore, unless explicitly specified, only real valued functions will be considered in this article.The domain of a function of several variables is the subset of ℝn for which the function is defined. As usual, the domain of a function of several real variables is supposed to contain an open subset of ℝn.