By John H. Hubbard, Beverly H. West
MacMath is a systematic toolkit for the Macintosh computing device which include twelve snap shots courses. It helps mathematical computation and experimentation in dynamical structures, either for differential equations and for generation. The MacMath package deal used to be designed to accompany the textbooks Differential Equations: A Dynamical structures strategy half I & II. The textual content and software program used to be constructed for a junior-senior point path in appropriate arithmetic at Cornell college, so one can benefit from very good and simply available images. MacMath addresses differential equations and generation equivalent to: analyzer, diffeq, section airplane, diffeq 3D perspectives, numerical equipment, periodic differential equations, cascade, second generation, eigenfinder, jacobidraw, fourier, planets. those flexible courses vastly improve the knowledge of the maths in those subject matters. Qualitative research of the image results in quantitative effects or even to new arithmetic. This new version comprises the newest 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™
To Find the Roots of the Graph First, select the function as explained above. Then choose IFind Rootsl from the ITask I menu. The roots of the original entered function (if they exist) will be displayed in the Root(s) window. You will be given a choice between two methods: • Bisection method will find all at once the roots on the screen by looking for places where the function goes from positive to negative and narrowing in on the root. How close it comes to the root is determined by the ITolerance for Bisectionl, which you can change using the IChange I menu.
Jectory as t increases. 59 MacMath 60 How It Works When first prompted for the equations in DIFFEQ, PHASE PLANE, enter functions that depend only on x and y, but not on t, because only in the autonomous case does the phase plane make good sense. Please refer to Section 5, General Overview, for instructions on entering functions and on features common to all programs. To Draw a Solution Choose IDraw trajectory I from the ITasks I menu, then select a point through which a trajectory is to be drawn by moving the cursor to the point of interest and clicking.
NAN stands for "not a number" . • Most items under the IEdit I menu are disabled unless you are using a IDesk Accessoryl from the. menu. • Many menu options have ):: C and a letter next to them. J COPY GRAPH I~ ITERATE [gIJ GI 5. General Overview of Program Operation LOCATESINGULAJUTY [gIJ CHANGE MATRIX 1:l=C MI OPEN 1:l=C 0 I PRINT something ~ QUIT PROGRAM 1:l=C Q I REMOVE something 1:l=C R I SAVE AS [gTI RESET whatever 1:l=C T I CLEAR/ERASE ALL 1:l=C u I PASTE 1:l=C V I CUT 1:l=C X I ERASE LAST whatever 1:l=C y I UNDO ~ EXIT whatever ~ 37 All the programs have the following menu bar: FILE EDIT I CHANGE TASKS I SETTINGS I CLEAR On the following page is a list of common menu elements, but individual programs will have additional ones.