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Unformatted text preview: AM 351 Assignment No. 6 Fall 2005 Systems of First Order Linear DEs Due: Tuesday, November 21, 2005, 1:30 p.m. (under my door) 1. Construct the first three iterates u , u 1 and u 2 of Picard’s method of successive substitution applied to the following linear system IVP: " x 1 x 2 # = " 1- 1 #" x 1 x 2 # , " x 1 (0) x 2 (0) # = " 1 # . (1) (Work on each component x i separately.) Compare your results with the solution of the IVP. 2. In Assignment No. 5, you determined the fundamental matrix Φ( t, 0) for the linear system defined by x = Ax where A = "- 3 2 2- 3 # . (2) Of course, we now know that Φ( t, 0) = e t A . Find e t A via an appropriate similarity transformation B = C- 1 AC . 3. Find the constant matrix A corresponding to the linear system x = Ax that has the following general solution: x ( t ) = C 1 e- 2 t 1 1 ! + C 2 e- t 1- 1 ! . (3) Explain briefly the basis of your solution. 4. Course Notes, Problem Set 3, No. 2. (You can solve for x 1 ( t ) and then use this result to solve for x 2 ( t ).) 5. The force on a charge q due to the presence of an electrostatic field E and a magnetic field B is given by F = q E + q c v × B , where v denotes the velocity of the charged particle and...
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This note was uploaded on 09/20/2010 for the course AMATH 351 taught by Professor Sivabalsivaloganathan during the Spring '08 term at Waterloo.
- Spring '08