! ! ! ! Instructions for Use! ! ! ! ! ! ! ! ! ! ! !!!!!!!!!!!!Grapher! !!!!!!!!!!!Versions 1.1 2.0 2.1! !!!!!!!!!!!!!! 2.2 2.3 2.5 ! !!!!!!!!!!!(and old Curvus Pro X 1.3.2)! ! ! ! ! ! ! (including a list of bugs and their workarounds)! ! ! “ When everything else fails, read the instructions “! ! !!!!!!!!!!April 16th 2014 edition" #1 ! Contents! ! ! page! ! Overview of Grapher! !! Summary!..........................................................................................................................4! !! Intuitive user interface!.......................................................................................................4! !! Inspectors!.........................................................................................................................5! !! Intuitive syntax!..................................................................................................................5! !! Animations!........................................................................................................................6! !! 3D view!.............................................................................................................................7! !! Export your creations!........................................................................................................7! !!! Contextual menus!.............................................................................................................7! ! Initiation! !! Lesson 1 : Creating a document!.......................................................................................8! !! Lesson 2 : Customizing the appearance of a document!.................................................11! !! Lesson 3 : Creating an animation (Animate Parameter)!.................................................15! !! Lesson 4 : Differential equations!....................................................................................20! !! Lesson 5 : Creating an animation (Create Animation) 2D and 3D!..................................27! !!! Lesson 6 : Treating a point set (Regression curve)!........................................................31! ! Grapher’s coordinate systems! !! 2D coordinates!................................................................................................................38! !!! 3D coordinates!................................................................................................................39! ! Expressions! !! Expressions syntax : general rules!.................................................................................41! !! Curves!............................................................................................................................43! !! Surfaces!..........................................................................................................................43! !! Fields!..............................................................................................................................44! !! Solutions to inequalities!..................................................................................................44! !! Constant expressions!.....................................................................................................44! !! Definitions of functions!....................................................................................................45! !! Point set data!..................................................................................................................45! !! Integrals and derivatives!.................................................................................................46! !! Sum, product, factorial, binomial coefficient, rounding, modulo, iteration!.......................47! !! Matrices and determinants!.............................................................................................47! !! Differential equations!......................................................................................................47! !! Sequences!......................................................................................................................48! !!! “Syntax error“ signal!.......................................................................................................48! ! Using the equation editor! !! Entering new data into the list of equations!....................................................................49! !! Sources of signs and symbols!........................................................................................49! !! Comments entered by the equation editor!......................................................................50! !! Navigating the equation editor!........................................................................................50! !! Exporting an equation!.....................................................................................................50! !! Keyboard shortcuts for the equation editor!...............................................................51! !! Built-in definitions!........................................................................................................53! ! #2 ! Numerical calculations (evaluations) ! !! Numerical evaluation of constant expressions!...............................................................55! !! Numerical evaluation of functions!...................................................................................55! !! Numerical evaluation of fields!.........................................................................................56! !! Numerical evaluation of sequences!................................................................................57! !! Numerical evaluation of point sets!..................................................................................57! !!! Calculation accuracy!.......................................................................................................57! ! Layout, appearance, saving and exporting the document! !! Opening a new document!...............................................................................................59! !! Formatting axes, grid and frame of the graph!.................................................................59! !! Customizing curves, surfaces and points!.......................................................................60! !! Adding objects to a 2D graph!.........................................................................................60! !! 3D graphs: perspective and appearance options!...........................................................61! !! Other uses!......................................................................................................................61! !! Informations to note before saving a 2D document!........................................................62! !!! Saving, exporting, templates!..........................................................................................62! ! Grapher’s bugs! !! A bit of history!.................................................................................................................63! !!! Grapher’s bugs and their workarounds!..........................................................................63! ! Appendices! !! Appendix 1. Point sets: from spreadsheets to Grapher!..................................................69! !! Appendix 2. Adaptation of lesson 4 in Grapher 2.0!........................................................70! !! Appendix 3. Calculations with complex numbers!...........................................................71! !! Appendix 4. Indexed expressions!...................................................................................73! !! Appendix 5. Matrices and determinants : solutions of linear equations!..........................74! !! Appendix 6. Expression syntax : supplements!...............................................................75! !! Appendix 7. Surfaces of revolution from a 2D curves!.....................................................77! !! Appendix 8. Changing files from Curvus Pro X (.cpx) to Grapher (.gcx)!........................78! !! Appendix 9. Matrices in Grapher!....................................................................................! 79! ! ! ________________________________! ! ! ! Despite its bugs (with their workarounds), Grapher is an outstanding software that should please you. I !wish you as much fun as I’ve experienced using it.! !!!!!!!!!!!!Yves Barois! ! ! This manual (French and English versions), English documentation on Internet, various works built with Grapher, are available on :! ! ! <http://y.barois.free.fr/grapher/>" #3 Overview of Grapher! Summary.! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Grapher is software specifically designed for Mac OS X to show various graphic representations of equations. It can graph the following mathematical expressions :! !• Explicit or implicit equations! !• Parametric curves and surfaces! !• Solutions of differential equations! !• Discrete sequences! !• Scalar and vector fields! !• Inequalities and Boolean equations! ! • Sets of points! Grapher presents a convivial interface which allows to quickly create professional-quality graphs. Moreover, it provides additio- nal tools such as :! !• Evaluation and integration! !• Animation! !• Regression curves! !• etc.! ! !Intuitive user interface.! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! #4 !Toolbar : ➊.! Use the toolbar to select the action of the cursor, to change the limits of the frame, to show the inspectors, etc..! ! To customize