Constructadirect(butunmotivated)proofofExample1asfollows,w

Partial Differential Equations: An Introduction | 2nd Edition | ISBN: 9780470054567 | Authors: Walter A. Strauss

ISBN: 9780470054567 222

Solution for problem 3 Chapter 11

Partial Differential Equations: An Introduction | 2nd Edition

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Problem 3

Constructadirect(butunmotivated)proofofExample1asfollows,without using any knowledge of eigenvalues. Let w(x) be aC2 function such that w(0)=w(1)=0. (a) Expand 1 0 [w(x)w(x)cot(x)]2 dx and integrate the cross-term by parts. (b) Show that w2(x)cotx 0 asx 0 or 1. (c) Deduce that 1 0 [w(x)]2 dx2 1 0 [w(x)]2 dx = 1 0 [w(x)w(x)cot x]2 dx0. (d) Showthatifw(x)=sinx,thenpart(c)isanequalityandtherefore the minimum of Example 1 is 2.

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Math 1550 - 004 Spring 2017 Exam I Review We'll do our first midterm test on Friday, February 17 . Sections that will be tested on this exam:  0.1: Linear Equations a. Be able to solve Applied Linear Expression Problems (Mixture, Distance, Geometry)  0.2: Quadratic Equations a. Know the Quadratic Formula (I will not ask you to find complex roots on this exam) b. Know the Principle of Zero Product  0.3: Other Types of Equations a. Know Absolute Value Function b. Be able to find the roots of quadratic expressions (I don't care what method you use) c. Be able to solve Radical and Rational Expressions  0.4: Inequalities

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Chapter 11, Problem 3 is Solved

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Textbook: Partial Differential Equations: An Introduction

Edition: 2

Author: Walter A. Strauss

ISBN: 9780470054567

The full step-by-step solution to problem: 3 from chapter: 11 was answered by , our top Math solution expert on 01/05/18, 06:22PM. This textbook survival guide was created for the textbook: Partial Differential Equations: An Introduction, edition: 2. Partial Differential Equations: An Introduction was written by and is associated to the ISBN: 9780470054567. The answer to “Constructadirect(butunmotivated)proofofExample1asfollows,without using any knowledge of eigenvalues. Let w(x) be aC2 function such that w(0)=w(1)=0. (a) Expand 1 0 [w(x)w(x)cot(x)]2 dx and integrate the cross-term by parts. (b) Show that w2(x)cotx 0 asx 0 or 1. (c) Deduce that 1 0 [w(x)]2 dx2 1 0 [w(x)]2 dx = 1 0 [w(x)w(x)cot x]2 dx0. (d) Showthatifw(x)=sinx,thenpart(c)isanequalityandtherefore the minimum of Example 1 is 2.” is broken down into a number of easy to follow steps, and 61 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 14 chapters, and 657 solutions. Since the solution to 3 from 11 chapter was answered, more than 250 students have viewed the full step-by-step answer.