1.2

# 1.2 - Numerical Analysis Taylor Polynomial written by...

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Unformatted text preview: Numerical Analysis - Taylor Polynomial written by Soyoung Ahn 1 Intermediate Value Theorem  continuous on     min  ∈      max  ∈    ⇒ For any  ∈    , there exists  ∈   such that    . Mean Value Theorem  continuous and differentiable on   ⇒ There exists  ∈   such that      ′    . Integral Mean Value Theorem  continuous on    nonnegative and integrable on   ⇒ There exists  ∈   such that             . CHAPTER 1. TAYLOR POLYNOMIAL 1.1 The Taylor Polynomial ex > Find a linear polynomial    for which         ′    ′  for a given function  . ⇒         ′  .     and    :      ex > Find a quadratic polynomial for which             ′    ′    ″    ″  for a given function  . ⇒         ′          ″  .     and    :           ex >     and    : Find a polynomial of degree  for which           for all  ≥  . ⇒                         ⋯                 Numerical Analysis - Taylor Polynomial written by Soyoung Ahn 2 Taylor polynomial of degree  :           ⇒ polynomial of degree...
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## This document was uploaded on 10/18/2010.

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1.2 - Numerical Analysis Taylor Polynomial written by...

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