By John H. Hubbard, Beverly H. West
MacMath is a systematic toolkit for the Macintosh computing device including twelve pictures courses. It helps mathematical computation and experimentation in dynamical structures, either for differential equations and for new release. The MacMath package deal was once designed to accompany the textbooks Differential Equations: A Dynamical structures method half I & II. The textual content and software program was once constructed for a junior-senior point path in acceptable arithmetic at Cornell collage, with a purpose to make the most of very good and simply obtainable pictures. MacMath addresses differential equations and new release similar to: analyzer, diffeq, section airplane, diffeq 3D perspectives, numerical tools, periodic differential equations, cascade, second generation, eigenfinder, jacobidraw, fourier, planets. those flexible courses significantly improve the knowledge of the math in those issues. Qualitative research of the image results in quantitative effects or even to new arithmetic. This new version contains the most recent model of the Mac Math diskette, 9.2.
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Extra resources for MacMath 9.2: A Dynamical Systems Software Package for the Macintosh™
The reason is that there are only 300 pixels across the screen, so the computer plots only 300 points - not enough to give a true picture of this graph. The Equations AN ALYZER can handle up to six different functions at anyone time. They are listed on the IChange I menu, in the colors in which they will be graphed. ~ 1 black ~ 2 magenta ~ 3 blue ~ 4 red ~ 5 green ~ 6 cyan 6. Analyzer 41 The function that is currently active has its equation at the top of the drawing window. You can activate a function either by choosing it from the IChange I menu or pressing its J::I:-number key combination.
Clear the IMin/Max I or ~ window, then check, under the ISettings I menu, either IShow Newton's Approximationsl or ISee Iteration Valuesl. The List window will now be headed by IApprox. Roots I or IIteration I, respectively. To Clear the List Window Choose IClear List Window I from the IClear I menu, whichever list is currently on the screen: Roots, Min/Max, Approx. Root(s), or Iterations. To Change the Displayed Number of Digits Choose INumber of Decimal Digits Displayedl from the IChange I menu, which tells how many digits are to be displayed in the IRoot(s) I or IMin/Max I window; the default is 5 (if you choose 7 or 8, one or more digits may be hidden at the right side of the window).
ISo1'nl should be left if you do not know the exact numerical solution. The program then will calculate a bound on the error from the value at k steps compared with the value at 2k steps. However, if the exact solution is known, and entered numerically, exact error will be calculated and displayed (with two digits, in scientific notation). m To Change the Approximation Method The default method that the program uses to calculate trajectories is RungeKutta. Choose IChange Method I under the IChange I menu and click on Euler or Midpoint Euler to change it.