{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

TAM310hw06

# TAM310hw06 - x ±ind the Frst 4 nonzero terms 2b...

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

TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand Homework No.6 (Due Tuesday March 4) 1. We have seen in class that the equation xy primeprime + y prime + xy = 0 (1) has the general solution y = c 1 J 0 ( x ) + c 2 Y 0 ( x ) (2) where J 0 ( x ) is the Bessel function of order zero of the first kind, and where Y 0 ( x ) is the Bessel function of order zero of the second kind. See for example my online notes, eq.(130), or Edwards and Penney, section 8.4, example 3. These Bessel functions can be generated in MATLAB using the notation besselj(0,x) and bessely(0,x). (Type “help bessel” in MATLAB.) 1a. In MATLAB, plot J 0 ( x ) and Y 0 ( x ) from x=0 to x=30. Hand in a copy of your plot. 1b. Use MATLAB to find the first zero of J 0 ( x ) to 8 significant figures. 2. A more general version of Bessel’s equation (1) is: x 2 y primeprime + xy prime + ( x 2 - p 2 ) y = 0 (3) See Edwards and Penney, section 8.5. Eq.(3) has a solution J p ( x ) which reduces to J 0 ( x ) when p = 0. 2a. Use the method of Frobenius to obtain a series solution for
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x ). ±ind the Frst 4 nonzero terms. 2b. Di²erentiate your result of 2a and show that d dx ( xJ 1 ( x )) = xJ ( x ) (4) 2c. Similarly di²erentiate the series for J ( x ) and show that d dx ( J ( x )) =-J 1 ( x ) (5) 2d. In MATLAB, plot J ( x ) and J 1 ( x ) from x=0 to x=30 on the same plot. Hand in a copy of your plot. 3. Using the search engine GOOGLE, search for an application of Bessel functions to a topic that you are interested in. ±or example, googling “blood ³ow Bessel” comes up with a number of references of mathematical models of blood ³ow which involve Bessel functions. ±rom the various hits google delivers, choose one and write a paragraph describing the application and how Bessel functions enter into the analysis. Print out a sample page of the application and include it with your homework....
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