Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 11.3, Problem 14E
In Problems 11–24 expand the given function in an appropriate cosine or sine series.
14.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
2) Perform the following index shifts:
no anx as a series that starts at n = 2
i. Write y =
ii. Write y =
-2an (x + 1)" as a series that starts at n = 0
iii. Write y = E=3(−1)″ (x − 4)¹ as a series that starts at n = 0
1
iv. Write y =
as a series that starts at n = 5
n=1
3n-1
v. Write y = Σo(-1)" as a series that starts at n = 2
Question 9
Find the derivative of following series:
Σ
(k + 2) 2*
xk+1
(k + 1) (k + 2) 2k
xk=1
b) O
(k + 2) 2k
kxk-1
(k + 2) 2k
k?xk-1
Σ
(k + 2) 2k-1
d)
1
e) O2
k(k + 2)²2k-1
Question 9
10. Find a power series representation for the function f(x)
1
x + 5
Chapter 11 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - In Problems 712 show that the given set of...Ch. 11.1 - In Problems 712 show that the given set of...Ch. 11.1 - In Problems 712 show that the given set of...
Ch. 11.1 - In Problems 712 show that the given set of...Ch. 11.1 - In Problems 712 show that the given set of...Ch. 11.1 - In Problems 13 and 14 verify by direct integration...Ch. 11.1 - In Problems 13 and 14 verify by direct integration...Ch. 11.1 - Let {n(x)} be an orthogonal set of functions on...Ch. 11.1 - Let {n(x)} be an orthogonal set of functions on...Ch. 11.1 - Let {n(x)} be an orthogonal set of functions on...Ch. 11.1 - From Problem 1 we know that f1(x) = x and f2(x) =...Ch. 11.1 - A real-valued function is said to be periodic with...Ch. 11.1 - A real-valued function is said to be periodic with...Ch. 11.1 - Prob. 21ECh. 11.1 - A real-valued function is said to be periodic with...Ch. 11.1 - A real-valued function is said to be periodic with...Ch. 11.1 - A real-valued function is said to be periodic with...Ch. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Relate the orthogonal set B in Problem 27 with a...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 1–16 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - Prob. 13ECh. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 116 find the Fourier series of f on...Ch. 11.2 - In Problems 17 and 18 sketch the periodic...Ch. 11.2 - In Problems 17 and 18 sketch the periodic...Ch. 11.2 - Use the result of Problem 5 to show that...Ch. 11.2 - Prob. 20ECh. 11.2 - Use the result of Problem 7 to show that...Ch. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.3 - In Problems 110 determine whether the function is...Ch. 11.3 - Prob. 2ECh. 11.3 - In Problems 110 determine whether the function is...Ch. 11.3 - In Problems 110 determine whether the function is...Ch. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - Prob. 15ECh. 11.3 - In Problems 11-24 expand the given function in an...Ch. 11.3 - Prob. 17ECh. 11.3 - In Problems 11-24 expand the given function in an...Ch. 11.3 - In Problems 11-24 expand the given function in an...Ch. 11.3 - In Problems 1-10 determine whether the function is...Ch. 11.3 - In Problems 1-10 determine whether the function is...Ch. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - In Problems 1124 expand the given function in an...Ch. 11.3 - Prob. 24ECh. 11.3 - In Problems 2534 find the half-range cosine and...Ch. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - In Problems 2534 find the half-range cosine and...Ch. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - In Problems 2534 find the half-range cosine and...Ch. 11.3 - In Problems 2534 find the half-range cosine and...Ch. 11.3 - Prob. 34ECh. 11.3 - In Problems 3538 expand the given function in a...Ch. 11.3 - In Problems 3538 expand the given function in a...Ch. 11.3 - Prob. 37ECh. 11.3 - In Problems 3538 expand the given function in a...Ch. 11.3 - Prob. 39ECh. 11.3 - In Problems 3942 suppose the function y = f(x), 0 ...Ch. 11.3 - In Problems 3942 suppose the function y = f(x), 0 ...Ch. 11.3 - Prob. 42ECh. 11.3 - In Problems 43 and 44 proceed as in Example 4 to...Ch. 11.3 - In Problems 43 and 44 proceed as in Example 4 to...Ch. 11.3 - Prob. 45ECh. 11.3 - Prob. 46ECh. 11.3 - Suppose a uniform beam of length L is simply...Ch. 11.3 - Prob. 50ECh. 11.3 - Prob. 51ECh. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.4 - Consider y + y = 0 subject to y(0) = 0, y(L) = 0....Ch. 11.4 - Consider y + y = 0 subject to the periodic...Ch. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - (a) Find the eigenvalues and eigenfunctions of the...Ch. 11.4 - (a) Find the eigenvalues and eigenfunctions of the...Ch. 11.4 - Laguerres differential equation xy + (1 x)y + ny...Ch. 11.4 - Hermites differential equation y2xy+2ny=0,n=0,1,2,...Ch. 11.4 - Consider the regular Sturm-Liouville problem:...Ch. 11.4 - (a) Find the eigenfunctions and the equation that...Ch. 11.4 - Prob. 13ECh. 11.5 - Prob. 1ECh. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - In Problems 36 expand f(x) = 1, 0 x 2, in a...Ch. 11.5 - In Problems 36 expand f(x) = 1, 0 x 2, in a...Ch. 11.5 - In Problems 7-10 expand the given function in a...Ch. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - In Problems 15 and 16 write out the first five...Ch. 11.5 - Prob. 16ECh. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.5 - Prob. 19ECh. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Prob. 23ECh. 11.5 - Prob. 24ECh. 11 - In Problems 16 fill in the blank or answer true or...Ch. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Consider the portion of the periodic function f...Ch. 11 - Prob. 19RECh. 11 - Find the eigenvalues and eigenfunctions of the...Ch. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 4. Show that inf {1+ 1/n : n e N} = 1arrow_forwardProblem 3: Show that for n ≥ 1, L. dx (1+x²)n+1 1.3.5... (2n-1).. 2.4.6... (2n)arrow_forward4. Expand F. (X) = .03.X as a half range Fourier... Sine.... 5 series in the range FX F. π..... 8 3 ans: f(x) = $ (= sinex + 2 sinux +. ..s.in.b. X. +. -----) 15 35arrow_forward
- 2 3. Find the Fourier Cosine Series of f(x) = 4x; 0 < x < 1arrow_forward.15 What is the coefficient of x'y5 in the expansion of (1x + 3y)18?arrow_forward4. Find a geometric power series for the functions, centered at c = 0 unless a different c is specified. a. f(x)= b. f(x)=· -,c=2 1 2-x 3 2x-1' f. f(x) = g. f(x) = 3 2x-1 3x x²+x-2arrow_forward
- In Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 4. x" + 25x = 90 cos 41; x (0) = 0, x'(0) = 90arrow_forwardIn Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 3. x" + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375, x'(0) = 0arrow_forwardpage 8 8. Given the function f(x) In(x-1). (a) Find the general formula for f(" (x), that is, find the nth derivative of f(x). Show your work! (b) Use (a) to find the Taylor series for f(x) centered at a = 6. Show your work!arrow_forward
- Problem 1: 1. Consider the function 0 if 1 if 0 if -3≤ x < -1, −1≤ x < 1, 1 ≤ x < 3; a) Sketch the graph of f on the interval [-7,7]. f(x) = f(x + 6) = f(x). b) Find the Fourier series for f. Explain why the series converges to 0.5 when x = 7.arrow_forward1. Use a substitution to find (6x? + 2)e"*+¤ dx showing working.arrow_forward6. Find the first three nonzero terms of the power series in powers of x of the function f (x) = x2-1 1-5x %3D O f (x) = -1 + 5x – x² + .. ... None of them O f (x) = -1 + 5x – x² + .. O f (x) = -1 –- 5x + x² + .. %3D O f (x) = 1 + 4x – x² + --arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
But what is the Fourier Transform? A visual introduction.; Author: 3Blue1Brown;https://www.youtube.com/watch?v=spUNpyF58BY;License: Standard YouTube License, CC-BY