Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Periodic Functions: Limits and Compositions

In course

MATH-101(g): Analysis I

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable. ...

Description

This lecture covers the concepts of periodic functions, functions defined by pieces, and limits of functions at a point. It also explores the composition of functions, with examples illustrating the properties of even and odd functions. The instructor discusses the properties of hyperbolic functions and their algebraic operations, as well as the periodicity of functions and their compositions.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (2)

Annalisa Buffa

Lénaïc Chizat

Official source

Related concepts (31)

Hyperbolic functions

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola. Also, similarly to how the derivatives of sin(t) and cos(t) are cos(t) and –sin(t) respectively, the derivatives of sinh(t) and cosh(t) are cosh(t) and +sinh(t) respectively. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry.

Lemniscate elliptic functions

In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied by Giulio Fagnano in 1718 and later by Leonhard Euler and Carl Friedrich Gauss, among others. The lemniscate sine and lemniscate cosine functions, usually written with the symbols sl and cl (sometimes the symbols sinlem and coslem or sin lemn and cos lemn are used instead), are analogous to the trigonometric functions sine and cosine.

Even and odd functions

In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are named for the parity of the powers of the power functions which satisfy each condition: the function is an even function if n is an even integer, and it is an odd function if n is an odd integer.

Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.

Transcendental function

In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically. Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Formally, an analytic function f (z) of one real or complex variable z is transcendental if it is algebraically independent of that variable.

Related lectures (37)

Algebraic Operations MOOC: Analysis I MOOC: Analysis I (part 4) : Limit of a function, continuous functions

Explores algebraic operations on functions, even and odd functions, and periodic functions.

Derivatives and Functions

Covers the theorem of the intermediate value, corollaries, and geometric interpretation of derivatives.

Functions of Several Real Variables

Explores real functions of several real variables, limits, and algebraic operations.

Hyperbolic Functions

Covers hyperbolic functions, including definitions, properties, and derivatives, explained with detailed examples and derivations.

Algebraic Operations on Limits MOOC: Analysis I MOOC: Analysis I (part 4) : Limit of a function, continuous functions