MATH 400 Midterm: MATH 400 2011 Winter Test 1
Document Summary
Rules governing examinations (cid:149) each candidate must be prepared to produce, upon request, a. [20] consider the equation for ( ) : Page 3 of 8 pages: [20] (i) find the (implicit) solution to the equation: Nd and sketch the shock trajectory and characteristics. 2 + 2 + 2 = 0 (i) classify the equation and put in canonical form. (ii) find the general solution. Page 6 of 8 pages: [20] consider the eigenvalue problem: = 0 1 . (1) = 0 0( ) = 0 (i) write the problem in sturm-liouville form and state the orthogonality condition. (ii) prove (without solving the equation explicitly) that the eigenvalues satisfy 0. (iii) determine the eigenvalues and eigenfunctions explicitly. Page 7 of 8 pages: [20] suppose ( ) satis es. + = 0 0 0 . Bounded as . (i) find ( ) using separation of variables for general ( ) and write the solution in the form.
