{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Homework_5_Spring_2010

# Homework_5_Spring_2010 - 6 4 1 3 1 2 1 1 1 2 2 2 2 2 5 Show...

This preview shows page 1. Sign up to view the full content.

1 MAE 105: Introduction to Mathematical Physics Homework 5 Posted: May 4, 2010 , DUE: May 14, 2010 (Friday, 1 pm), 1. Write down the Fourier series representation for the following function, f(x) defined as follows: x x x x f 2 , 0 2 0 , 1 0 , 0 ) ( Is this an even or an odd function? Why? 2. Write down the Fourier series representation for the following function, f(x) defined as follows: x x x x f 0 , sin 0 , 0 ) ( (a) Why does the above function have both sine and cosine terms in the Fourier series? (b) Describe how you could represent the function f(x) = sin ( x ) , 0 < x < only with cosine terms? 3. Expand f(x) = x 2 , 0 < x < 2 in a Fourier series, if (a) the period is 2 Additionally, what is the value of f(x) at x= 0 and x = 2 ? (b) the period is not specified. 4. Using the results of Problem 3, prove that
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 6 ... 4 1 3 1 2 1 1 1 2 2 2 2 2 5. Show, graphically, that a Fourier series can only be differentiated if f ( x ) is continuous and f (0) = f ( L ) = 0. Consequently, verify that the temperature distribution in a one-dimensional rod (that we previously derived in class) could be expanded in terms of a Fourier sine series, if and only if both ends of the rod have a temperature of zero. 6. Show (using the de Moivre relations) that an alternate representation of the function, f(x) expressed as a Fourier series over an interval (-L, L ), i.e., f(x) ~ ) sin( ) cos( 1 1 L x n b L x n a a n n n n o is: f(x) ~ ) ( L x n i n n e c where ) ( 2 1 n n n b i + a c...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern