Lecture

Taylor Polynomials and Remainders

Related lectures (31)

Taylor Polynomials: Approximating Functions with Taylor Polynomials

Delves into Taylor polynomials, showcasing how higher orders improve function approximations and how they can be used to calculate limits.

Solving the Quintic: Dominant Balance Analysis

Explores dominant balance analysis in solving the quintic polynomial, revealing insights into root behavior and the importance of symbolic expressions.

Approximation of Functions by Taylor Polynomials

Explores the theory and application of Taylor polynomials for function approximation and limit calculations.

Taylor Polynomials: Calculating Limits and Derivatives

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Derivation and Integration Rules in Analyse 2

Explores derivation and integration rules for Taylor polynomials, showcasing iterative methods to calculate functions like ln(x) and arctan(x).

Taylor Polynomials: Examples and Convergence

Covers examples of Taylor polynomials and discusses their convergence when approximating functions.

Taylor Polynomials: Approximating Functions

Introduces Taylor polynomials for approximating functions around a point, showcasing their importance in accurately representing functions.

Taylor Series: Approximating Functions with Polynomials

Explores approximating functions with polynomials using Taylor series and discusses the convergence of series representations.

Transforms of the Place

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Mathematics: Analysis and Algebra Overview

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Taylor Polynomials: Correction Term

Explores the correction term in Taylor polynomials, showcasing its role in refining function approximations.

Taylor Development: Higher Derivatives

Covers the calculation of Taylor polynomials, higher derivatives, and Taylor series using examples.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Developing Cosine Composition

Explores the composition of Taylor expansions through an example, simplifying complex compositions to identify essential terms.

Lagrange Interpolation

Introduces Lagrange interpolation for approximating data points with polynomials, discussing challenges and techniques for accurate interpolation.

Complex Numbers: Representations

Explores different ways to represent complex numbers, including geometric and trigonometric representations, simplifying calculations and enhancing intuition.

Functions n+1 Derivatives

Covers the concept of functions being n+1 times differentiable and the Taylor formula.

Division Euclidienne: Exemples

Explains the Euclidean division of polynomials and demonstrates its application through examples and root-based divisibility.

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Taylor Polynomial in Two Variables

Covers the Taylor polynomial in two variables and the concept of extrema in functions of several variables.