Problem Set #2

Module 2.4 Exercises: 4abcde on p. 65. For part e, I just googled on integration tool and found http://integrals.wolfram.com. You'll have to use x instead of t, and e^ for exponent. Then you can use Excel (EXP function for e^) or a scientific calculator to compute the final value, based on the Fundamental Theorem of Calculus (p. 62). 


Module 3.2 Exercise: 4cde on p. 84. This is a bit tricky because the initial value involves a subtraction (object's temperature T minus room temperature 25). Usually you'd have dT/dt = kT with solution T = T0ekt. But here the change is proportional not to T but to (T-25): dT/dt = k*(T-25), which is the answer to part (a). So how to solve this? If you're good at calculus, you could probably figure it out, but I'm not. So I used Mathematica (installed on the machines in Parmly 302, our lab). I eventually got it to tell me that the solution is T =(T0-25)ekt + 25, which is the answer to part (b). The (T0-25) part makes sense, because that's the initial condition of being 25 degrees off from room temperature. So I guess the + 25 part is saying that if the difference is 25, you've got add 25 back in to get the actual value. 


Module 3.3 Exercise: 5 on p. 93. I would use Excel to produce the graph (part a): Enter the numbers 0 through 10 in Column A, then in cell B1 type the formula = EXP(-A1), and copy-and-paste into the remaining cells in column B. Then do Insert/Scatter and choose the smooth-line plot. Then copy-and-paste the plot into your writeup. For 5b-f, Excel and Vensim can also help you to match the formulas (A-F) with the English descriptions (b-f),but all you need to turn in for these is the final answer (what goes with what).