m257_316_midterm1_sec101w2009

m257_316_midterm1_sec101w2009 - [5 marks] (c) Use the...

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

View Full Document Right Arrow Icon
Math 257/316, Midterm 1, Sections 101/102 19 October 2009 Instructions. The duration of the exam is 55 minutes. Answer all questions. Calculators are not allowed. Maximum score 80. 1. Consider the second order di f erential equation: Ly =6 x 2 y 00 + xy 0 +(1+ x ) y =0 (1) (a) Classify the points x 0 (including the point at ) as ordinary points, regular singular points, or irregular singular points. [10 marks] (b) If you were given y (1) = 1 and y 0 (1) = 2 , what form of series expansion would you assume (you need not determine the expansion coe cients of this series)? What would be the minimal radius of convergence of this series?
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: [5 marks] (c) Use the appropriate series expansion about the point x = 0 to determine two independent solutions to (1). You only need to determine the f rst three non-zero terms in each case. [35 marks] 2. Apply the method of separation of variables to determine the solution to the one dimensional heat equation with the following homogeneous Neumann boundary conditions: u t = 2 u x 2 , < x < , t > BC : u x (0 ,t ) = 0 = u x ( ,t ) IC : u ( x, 0) = 1 [30 marks] 1...
View Full Document

Ask a homework question - tutors are online