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Course: CS 383, Fall 2009
School: Sveriges...
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Sveriges lantbruksuniversitet - CS - 383
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Sveriges lantbruksuniversitet - CS - 383
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MS 238 Stochastic Processes, Spring 2008 Second Coursework, due Thursday 17 April1 A particle moves on the 4 vertices of a square in the following way: at each step the particle is equally likely to move to each of the two adjacent vertices. Comput
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MS 238 Stochastic Processes, Spring 2008 Exercise Sheet 21. Consider a random walk on the integers {0, 1, . . . , N} with absorbing states at 0 and N. Suppose a particle starts at position k and that the nonzero transition probabilities pij for i =
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MS 238 Stochastic Processes, Spring 2008 Exercise Sheet 31. A blackboard in the Department of Mathematics poses the following question about snakes. There are 237 snakes in a pit. A snakes head and a snakes tail are chosen at random (possibly belon
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MS 238 Stochastic Processes, Spring 2008 Exercise Sheet 41. A frog jumps on the vertices of a triangle. At each jump, it moves to one of the neighbouring vertices, but it is three times more likely to jump clockwise than counterclockwise. Find the
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MS213 Spring 2007, Exercises, 23 January 20071. 2. Compute the general solution to F = ma with m = 1 and F (x, v, t) = e-5t . Solve the IVP x = 3t + 1, x(0) = 2, x (0) = 33. Consider the ODE x = 9x . Find all values of the constants a, b, c for at
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MS213 Spring 2007, Exercises, 30 January 20071. Consider the following ODE: dx = x3 + x2 - 6x dt (i) Sketch the phase portrait. (ii) State which equilibria are attractors or repellors (or neither). (iii) Determine which equilibria are sinks and whic
East Los Angeles College - MS - 213
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MS213 Spring 2007, Exercises, 15 February 20071. Consider the following examples from the Revision exercises (16 January 2007): Q5(b), Q5(c), Q6(a), Q6(b). In each case, find a particular solution for the ODE using variation of parameters. 2. Solve
East Los Angeles College - MS - 213
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East Los Angeles College - MS - 213
MS213 Spring 2007, Exercises, 21 February 20071. Consider the system of ODEs x = A(t)x + E(t) where A(t) = Verify that x(t) = c1 t-1 -t-2 + c2 t-1 ln t -t-2 ln t + t-2 +1 -1 t (ln t)2 2 - 1 t-2 (ln t)2 + t-2 20 1 -t-2 -3t-1,E(t) =0 t-3.
East Los Angeles College - MS - 213
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East Los Angeles College - MS - 213
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East Los Angeles College - MS - 213
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East Los Angeles College - MS - 213
MS213 Spring 2007, Exercises, 13 March 20071. Sketch the phase portrait for the system x = Ax, A= 1 -2 3 0 .2.Sketch the phase portrait for the system x = Ax, A= 4 -2 2 0 .3.Sketch the phase portrait for the system x = Ax, A= -4 -1 3 0 .4.
East Los Angeles College - MS - 213
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East Los Angeles College - MS - 213
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East Los Angeles College - MS - 203
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