Lecture

Development Limit: Order 1 and 2

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In course

MATH-106(f): Analysis II

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs variables. ...

Description

This lecture covers the development of limited order 1 and 2, focusing on linearity and polynomial approximation. It explains the concepts of Taylor polynomials of order 1 and 2, linear approximation, and polynomial degree. The instructor discusses the development of limited order 1 and 2, emphasizing the linearity and approximation of functions around a point. The lecture also delves into the Taylor polynomials of order 1 and 2, showcasing their applications in function approximation.

Instructors (3)

Boris Buffoni

Research activityResearch ResearchCurrent Research Fields https://sma.epfl.ch/~buffoni/home.html Teaching & PhD Courses Analysis II MATH-106(b) The course studies fundamental concepts of analysis and the calculus of functions of several variables. Evolutional partial differential equations MATH-421 Fundamental techniques and theories for partial differential equations of evolution. Application to basic examples: first-order equations, wave equation, heat equation. The Cauchy

David Valentin Strütt

Assistanat Vous visitez cette page dans l'optique de rejoindre mon équipe d'asssistant·es pour un de mes cours d'analyse ? Vous trouverez plus d'informations ici. Contributions auteur de polycopiés d'analysecréateur matheminecraftrecord suisse du plus grand nombre de participations à la construction d'un additionneur binaire en dominos (autoproclamé) Je suis né pile le jour de mon anniversaire. Expériences professionnelles Chargé de communication pour MATH et chargé de cours pour la SMA 2019–2024 EPFLCharg

Adélie Eliane Garin

Teaching & PhD Courses Sustainability ENV-101 This course presents global sustainability issues. It introduces planetary boundaries, their systemic interconnections and social justice issues. The interdisciplinary approach introduces group work and systems thinking (interdependencies in a complex system). Sustainability in my research ENG-650 This course is designed to develop the necessary transversal skills to foster sustainability integration in the present and future rese

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Related concepts (32)

Polynomial

In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example with three indeterminates is x3 + 2xyz2 − yz + 1. Polynomials appear in many areas of mathematics and science.

Approximation theory

In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. What is meant by best and simpler will depend on the application. A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon summation of a series of terms based upon orthogonal polynomials.

Hermite polynomials

In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets for wavelet transform analysis probability, such as the Edgeworth series, as well as in connection with Brownian motion; combinatorics, as an example of an Appell sequence, obeying the umbral calculus; numerical analysis as Gaussian quadrature; physics, where they give rise to the eigenstates of the quantum harmonic oscillator; and they also occur in some cases of the heat equation (when the term is present); systems theory in connection with nonlinear operations on Gaussian noise.

Legendre polynomials

In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number of mathematical properties and numerous applications. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications. Closely related to the Legendre polynomials are associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, and associated Legendre functions.

Linear approximation

In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations. Given a twice continuously differentiable function of one real variable, Taylor's theorem for the case states that where is the remainder term.

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