Versions of MATHEMATICA

DEwM was written when the current version of MATHEMATICA was 6. You are almost certainly using a more current version -- possibly 7 and more likely 8. Fortunately, there have not been many changes in the software that affect the commands and code relevant to this ode course. Unfortunately, there have been some. In the roster below is a description of relevant changes, arranged more or less in the order in which you will encounter them as you progress through the course. Additional entries will be made if/as new discrepancies are uncovered. In particular, if you discover any other changes or problems with the software that are not accounted for in the list below, please bring them to Dr. Lipsman's attention. Thank you.

It is also worth pointing out that the most important change in the newest version (i.e., 8) is the much more robust palettes that are available. More importantly, in addition to beefing up the symbols and operations that are available, MATHEMATICA now has inside the Basic Math Assistant palette, a roster of Basic Commands. You can now enter commands like DSolve, not only by typing them in the Command Window, but alternatively by clicking on a palette element. The philosophy is that you spend less time reading manuals like DEwM and more time experimenting on your own to learn the software system.

Chapter 2, Section 2.3, p. 8: The BasicMathInput palette is now called the Basic Math Assistant. In Problem 12 of PSA, you're asked to access the "sum" symbol from that palette. Look under Calculator:Advanced.
Chapter 3: You will find that the syntax of some error and warning messages has changed. For example, try the command on line "In[50]" on p. 22. Sometimes commands that previously elicited warning messages no longer do; for example, sol4 on p. 54 or sol5 on p. 57. In general, you should pay close attention to these messages when they appear; they usually, although not always, contain useful information.
Chapter3, Section 3.10: The implication is that the command Clear will clear all variables and definitions. This is problematic. It is best to clear the specific variables that you want cleared, e.g., Clear[x,f]. The command Clear["Global`*"] will definitely clear everything, but you should use that command cautiously. You can always reset the kernel by following the instructions in Section 4.2.1, p. 33.
If I may quote from the help on the command N, "Unless numbers in 'expr' are exact, or of sufficiently high precision, N[expr,n] may not be able to give results with n-digit precision." An example may be found in Chapter 4. The input N[Sin[1/10], 20] yields 0.099833416646828152307; but the input N[Sin[0.1],20] yields 0.0998334.
Chapter 6 and PSB: The command VectorFieldPlot in the package VectorFieldPlots has been superseded by the built-in command VectorPlot. Alternatively, you may use the new command StreamPlot. In fact, you can continue to use the old command by loading the package with the command < < VectorFieldPlots`. MATHEMATICA warns you against using "obsolete" packages and commands, but apparently no harm ensues by doing so. The lengths of the vectors in a plot are better controlled by the option ScaleFunction in the old command than they are by the option VectorScale in the new comand. But the choice of which command to use is yours. This is the most serious change to ode commands that are used in this course.
PSB, Problem 14, parts (a) and (e): If in part (a), your output involves t^2 -C[1] instead of t^2 + C[1], then in part (e), change all minus signs to plus signs.
Chapter 7, Section 5 and PSC, Problem 8, Part (e): Dr. Lipsman has encountered some difficulties using AccuracyGoal. It might be a function of some settings in his machine. If you have difficulty in Problem C8(e), use the default accuracy.
Chapter 8, Section 8.12, p. 113: An alternate syntax for "In[64]" that you may find useful is
f[xval_, c_] := (y[x] /. First[NDSolve[{y'[x] == Sqrt[y[x] + x], y[1] == c}, y[x], {x, 1, 10}]]) /. x -> xval
Plot[Evaluate[Table[f[x, c], {c, 1, 5}]], {x, 1, 10}]
PSC, Problems 2 & 16: If you append a solution to Problem 16 to your solution of Problem 2, you will be awarded extra credit. The latter problem uses the "event detection" feature of MATHEMATICA, which remains unchanged in the new version.
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