22 Pages

CW1

Course: MS 238, Fall 2009
School: East Los Angeles College
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Word Count: 13487

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Coursehero >> California >> East Los Angeles College >> MS 238

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cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put readonly def /FontBBox{-36 -250 1070 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 36 /sterling put readonly def /FontBBox{-36 -251 1103 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 53 /five put dup 54 /six put dup 56 /eight put dup 61 /equal put dup 63 /question put dup 65 /A put dup 68 /D put dup 69 /E put dup 73 /I put dup 76 /L put dup 79 /O put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 124 /emdash put readonly def /FontBBox{-34 -251 988 750}readonly def currentdict end currentfile eexec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East Los Angeles College - MS - 238
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
East Los Angeles College - MS - 238
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East Los Angeles College - MS - 238
%!PS-Adobe-2.0 %Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %Title: Ex1.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 595 842 %DocumentFonts: CMBX12 CMR12 CMMI12 CMMI8 CMR8 CMSY10 CMTI12 %DocumentPaperSizes: a4 %EndComments %DVIP
East Los Angeles College - MS - 238
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 =
East Los Angeles College - MS - 238
%!PS-Adobe-2.0 %Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %Title: Ex2.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 595 842 %DocumentFonts: CMBX12 CMR12 CMSY10 CMMI12 CMMI8 CMR8 CMSY8 CMEX10 %DocumentPaperSizes: a4 %EndComments
East Los Angeles College - MS - 238
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
East Los Angeles College - MS - 238
%!PS-Adobe-2.0 %Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %Title: Ex3.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 595 842 %DocumentFonts: CMBX12 CMR12 CMMI12 CMSY10 CMEX10 CMR8 %DocumentPaperSizes: a4 %EndComments %DVIPSWebPa
East Los Angeles College - MS - 238
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
East Los Angeles College - MS - 238
%!PS-Adobe-2.0 %Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %Title: Ex4.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 595 842 %DocumentFonts: CMBX12 CMR12 CMSY10 CMMI12 CMMI8 CMR8 %DocumentPaperSizes: a4 %EndComments %DVIPSWebPag
East Los Angeles College - MS - 213
%!PS-Adobe-2.0 %Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %Title: CW1.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 595 842 %DocumentFonts: CMBX12 CMR12 CMMI12 CMR8 CMSY10 CMMI8 MSBM10 %DocumentPaperSizes: a4 %EndComments %DVIP
East Los Angeles College - MS - 213
%!PS-Adobe-2.0 %Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %Title: CW2.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 595 842 %DocumentFonts: CMBX12 CMR12 CMSY8 CMMI12 CMEX10 CMSY10 CMR8 MSBM10 %+ CMMI8 %DocumentPaperSizes: a4 %E
East Los Angeles College - MS - 213
MS213 Spring 2007, Revision exercises, 16 January 2007The questions below are taken from exercises given in Autumn 2006 for MS110 Matrices and Linear ODEs. dx =t, dt dx =x. dt1.Compute the general solution to(a)(b)2.Compute the general s
East Los Angeles College - MS - 213
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East Los Angeles College - MS - 213
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
East Los Angeles College - MS - 213
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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East Los Angeles College - MS - 213
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
MS213 Spring 2007, Exercises, 28 February 20071. Solve the system of ODEs x = Ax, A= 1 2 3 -4 .2.Solve the IVP x = Ax, 7 0 0 A = 1 -8 0 , 2 4 5 1 x(0) = 2 . 3 3.Solve the system of ODEs x = Ax, A= 2 -3 3 2 .4.Solve the systems of
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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East Los Angeles College - MS - 203
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East Los Angeles College - MS - 203
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East Los Angeles College - MS - 203
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East Los Angeles College - MS - 203
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East Los Angeles College - MS - 203
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