Open In App

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 7: Q21P (page 364)

Write out the details of the derivation of the formulas (8.3)

Short Answer

Expert verified

The value of coefficient is .

Step by step solution

Given information

Derivative formulas are given.

Concept of Fourier series

The Fourier expansion of function is

Apply integration

Integrate above function.

Integrate further as shown below.

Evaluate the complex version

The complex version is as follows:

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Following a method similar to that used in obtaining equations(12.11) to (12.14), show that if f(x)is even, then $g (α)$ is even too. Show that in this case f(x)and $g (α)$ can be written as Fourier cosine transforms and obtain (12.15).

The functions in Problems 1 to 3 are neither even nor odd. Write each of them as the sum of an even function and an odd function.

(a) $I n | 1 - x |$ (b) $(1 + x) (s i n x + c o s x)$

Let $f (t) = e^{i ω t}$ on $(- π, π)$ . Expand $f (t)$ in a complex exponential Fourier series of period $2 π$ . (Assume $w \neq$ integer.)

Sketch several periods of the corresponding periodic function of period $2 π$ . Expand the periodic function in a sine-cosine Fourier series.

f (x) = {\begin{cases} 1, - π < x < 0, . . . \\ 0, 0 < x < π, . . . . \end{cases}

In Problems 13to 16, find the Fourier cosine transform of the function in the indicated problem, and write f(x)as the Fourier integral [ use equation (12.15)]. Verify that the cosine integral for f(x)is the same as the exponential integral found previously.

14. Problem 7

See all solutions

Recommended explanations on Physics Textbooks

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free

Write out the details of the derivation of the formulas (8.3)

Short Answer

Step by step solution

Given information

Concept of Fourier series

Apply integration

Evaluate the complex version

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Physics of Motion

Electrostatics

Dynamics

Solid State Physics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

Company

Product

Help