by Jean Barbet | Dec 29, 2020 | Analysis, Functions, Non classé
Some functions that can be differentiated indefinitely can be described ‘around each point’ as the sum of an power series. These are analytic functions, real or complex, the typical example being the exponential function, which can be extended to the whole complex...
by Jean Barbet | Sep 16, 2020 | Algebra, Functions, Non classé
Polynomials with one variable are mathematical representations of the expressions used in polynomial equations. They allow algebraic methods to be applied to solving these equations. 1. Equations are “linguistic” objects 1.1 Polynomial equations and number...
by Jean Barbet | Jul 10, 2020 | Functions, Set Theory
A finite set is a set that can be counted using the natural numbers \(1,\ldots,n\) for a certain natural number \(n\). But what is counting ? And then, what is an infinite set? 1.Comparing sets : the notion of bijection The notions of finite set and infinite set, and...
by Jean Barbet | Jul 6, 2020 | Functions, Geometry
The definition of a circle is simple: it is a set of points located at the same distance from a given point. This distance is called the radius and this point is called the centre of the circle. The circle with centre \((-1,-3/2)\) and radius \(\sqrt 6\) 1. Circles as...
by Jean Barbet | Jun 25, 2020 | Functions, Geometry
The derivative of a function is its instantaneous variation, i.e. the slope of the tangent to the graphical representation of the function at that point. 1. General idea: an instantaneous variation We place ourselves here in the framework of functions of a real...