che132a-hw-2

che132a-hw-2 - λ =0,1,2,3,4 with Mathematica. Which...

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ChE132a: Analytical Methods of Chemical Engineering Professor Mike Gordon, Fall 2011 Homework #2: Due Friday 14 Oct. 2011 (1) PGA p. 43 #24, 25, 27, 30, 34, 41 (2) PGA p. 59 #10, 13, 19; use the method of undetermined coefficients (3) PGA p. 71 #1, 2; use variation of parameters (+ Mathematica for integrals) (4) Find all singular points and determine the radius of convergence (R) for the power series = = 0 ) ( n n n x c x y solution to the following ODEs. Do not solve the ODE or find n c ; I only want the singular points and R. (a) 2 ) sin( x y x y = + (b) 0 ) sin( = + u x u x be careful with this one (c) 12 4 * ) 2 cos( = + g g x (d) x e f x x f x = + - + 5 ) 2 ( 2 (5) Solve the following ODE using a power series expanded about x=0. Where is your power series solution valid? Make sure you split your series solution into its two linearly independent parts. 0 2 = - - y x y x y (6) Plot Bessel functions of the first and second kind of order
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Unformatted text preview: λ =0,1,2,3,4 with Mathematica. Which functions are odd and even? How are the two kinds different? Does anything “special” happen at x=0 in some cases? (7) What is the general solution to the following ODE (solve it by hand using the results from our in class derivations, i.e., don’t do through the derivation again)? ( 29 9 2 2 =-+ ′ + ′ ′ R r R r R r Plot the two linearly independent solutions with Mathematica. Apply the following boundary conditions and determine the final solution ) ( r R by hand: ) ( = R and 1 ) 1 ( ' = R Hint : use Mathematica to help you differentiate the general solution to learn something interesting about the general solutions of the above ODE…then plug in the 1 ) 1 ( ' = R condition....
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This note was uploaded on 12/29/2011 for the course CHE 132a taught by Professor Gordon,m during the Fall '08 term at UCSB.

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