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ProblemC3-2

# ProblemC3-2 - worksheet 3 Now substitute f 21 =16 f 12 =4 i...

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Computational Biology 03-310/510/710, Spring 2005 R. F. Murphy Page 1 of 1 Problem C3 Modeling compartmental systems Due: April 19, 2005 In this assignment we will solve simple compartmental systems using MAPLE. Consider the following compartmental system ( system 1 ) in which f 21 is the rate constant for transfer to compartment 2 from 1 and f 12 is the rate constant for transfer to compartment 1 from 2. Let q 1 (t) and q 2 (t) be the amounts of material at time t in compartments 1 and 2, respectively, and let q 1 (0)=i 1 and q 2 (0)=i 2 . Questions (Total of 40 points) Submit written/printed answers (a Word file containing both text and copies of plots is acceptable in place of written/printed answers) and an Maple workbook via the dropbox. 1. What is the timescale of system 1 ? 2. Using MAPLE, enter the differential equations describing system 1 without substituting values for the constants. Solve the set of equations using the dsolve procedure. Print or submit your maple
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Unformatted text preview: worksheet. 3. Now substitute f 21 =16, f 12 =4, i 1 =11, i 2 =1 and plot the solutions for q 1 (t) and q 2 (t) on the same axes (choose the most informative limits for the plot). Print or submit your maple worksheet. Print the plot and label the solutions. Extra Credit 6. ( 10 points ). Using MAPLE, enter the differential equations for system 2 (above) , solve it numerically (4/5 order Runge-Kutta method) and plot the solutions for q 1 (t) and q 2 (t) on the same axes (use f 02 =2). 7. ( 10 points ). Do Exercise 2, parts a-d , in Section 7.10 of Yeargers (p. 225). Submit your Maple worksheet(s) and written answers to the questions (either on paper or as a text file). 8. ( 10 points ). Do Exercise 1 in Section 7.11 of Yeargers (p. 232). Submit your Maple worksheet (and make sure that it includes a plot similar to Figure 7.11.2 but for the drug CPM). 1 f 21 2 f 12 → ← 1 f 21 2 f 12 → ← → f 02...
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