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

Lecture

Taylor Series: Development and Applications

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 study of local functions, behavior analysis, and the calculation of limits using examples. It also delves into Taylor series development, inflection points, and the application of Taylor's formula in various scenarios.

Instructors (2)

Lénaïc Chizat

Annalisa Buffa

Official source

Ontological neighbourhood

Mathematics

Analysis: Calculus

Related concepts (32)

Inflection point

In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (rarely inflexion) is a point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave (concave downward) to convex (concave upward), or vice versa.

Stationary point

In mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero. Informally, it is a point where the function "stops" increasing or decreasing (hence the name). For a differentiable function of several real variables, a stationary point is a point on the surface of the graph where all its partial derivatives are zero (equivalently, the gradient is zero).

Taylor series

In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century.

Taylor's theorem

In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the truncation at the order of the Taylor series of the function. The first-order Taylor polynomial is the linear approximation of the function, and the second-order Taylor polynomial is often referred to as the quadratic approximation.

Applied behavior analysis

Applied behavior analysis (ABA), also called behavioral engineering, is a psychological intervention that applies empirical approaches based upon the principles of respondent and operant conditioning to change behavior of social significance. It is the applied form of behavior analysis; the other two forms are radical behaviorism (or the philosophy of the science) and the experimental analysis of behavior (or basic experimental laboratory research).

Related lectures (36)

Taylor's Formula: Developments and Applications

Explores Taylor's formula, polynomials, functions, and series applications.

Taylor Series and Function Analysis

Explores Taylor series, function properties, inflection points, and critical points in graphical and mathematical contexts.

Taylor Polynomials: Special Cases

Explores Taylor polynomials, odd orders, simplification, residues, and special cases of zero polynomials.

Taylor's Formula: Developments and Extrema

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Partial Derivatives: Taylor Formula