¡Descarga Guia Maple para Novatos y más Apuntes en PDF de Informática solo en Docsity!
Maple Fundamentals Guide
© Maplesoft, a division of Waterloo Maple Inc.
This tutorial is designed to help you become familiar with the Maple environment and teach you fundamental concepts and tools you need to become productive quickly. To try this material on your own, start with an empty Maple document. Perform the steps found in the left column of each table below. The results of each step are displayed in the right column for your reference.
Note: This guide assumes you are working in Document mode. Most information applies equally to Worksheet mode, with minor visual differences. Any important differences are noted in the text.
Talking to Maple
Steps Results
Start Page
When you first open Maple, you will see the Start page. This page points you to a important resources for new users, and can be turned off later if desired. Click on the New Document icon, on the top left of the page to open a blank document.
Using [ENTER]
You can start by typing math into your Maple document and pressing [ENTER] in order to see the result.
Example: Type "1+2 [ENTER] ".
Notice that the result appears on the next line.
Using [Alt]+[ENTER]
If you would like to have the result returned on the same line, press [ALT]+[ENTER].
Example: Type "x+5-2" then [Alt]+ [ENTER].
Worksheet mode: Inline evaluation is not available in Worksheet mode. When working through this guide, simply press [ENTER] instead.
Changing the Problem
Math in a Maple document is live. You can go back, make changes, and re-execute the problem to obtain a new result.
Example: Go back to your original calculation of "1 + 2", change the number "1" to a "3" and press [ENTER]. Note the change in output.
Example: In the context panel example, above, change the "x" to "10 x". Highlight everything from "10 x" to the plot, then click the Execute selection button, ,
found on the toolbar at the top of the Maple window. All selected calculations are updated.
Tip: Clicking the Execute the entire worksheet button, , re-calculates the
entire document.
= integrate w.r.t. x
Smart Popups
At the top of the context panel, you'll find Smart Popups, which give you a preview of the result of an operation before you apply it.
Example: Enter sin(2x). From the
Context Panel, you can convert this
expression to an equivalent form using
trig identities.
full angle reduction identity: sin(2x)=2sin(x)*cos(x)
Entering Math
Steps Results
Entering Fractions Use / to enter a fraction. When you type /, you will automatically moved into to the denominator. Use the right-arrow key to come out again.
When your numerator contains multiple terms, you can use brackets to enclose the numerator...
...or you can select the terms you want, using the mouse or by holding down Shift and using the arrow keys, before pressing /. The selected expression will become the numerator of the fraction when you press /.
Palettes
Maple has over 1000 expressions and symbols within its collection of palettes, found on the left side of your Maple window. Some of them insert fill-in-the-blank templates into your document, and are useful for problem entry.
Example: Using the Expression Palette , find the definite integral of from 0 to
- Open the expression palette (click Expression on the left-hand side of your Maple document) and click the definite integral ( ) symbol. A definite integral
template will appear in your worksheet. Fill in the place-holders (use [TAB] to move to the next placeholder). When done, press [ENTER] to evaluate.
Important! Use ^ to create an exponent/superscript, and right-arrow to get out again.
Tip: You can put frequently used palette entries on the Favorites Palette. To do so, right-click on the desired expression in the palette and select Add to Favorites Palette.
Entering Symbols using Symbol Completion
You can enter common symbols, like or , using palettes. In addition, the symbol completion mechanism provides an alternative to palettes for entering symbols using the keyboard.
Type the first few characters of the symbol name, and press [Esc]. Choose the desired symbol from the list.
Example: Try entering. For the square root symbol, enter sqrt [Esc] and choose the symbol from the menu. Type e [Esc] for the exponential constant. To enter , type pi [Esc]. The right-arrow will take you outside the square root symbol.
Important! Use symbol completion to enter single letter symbols, such as the
exponential , the imaginary unit , and the
differential symbol. If you simply type , Maple will treat as a variable, like. Notice
the difference: (symbol) vs. (variable,
so is italicized).
The same mechanism can be used to enter templates.
Example: Type int [Esc]. Choices include various integration templates.
Multiplication
In the case of a number multiplied by a variable only, you have the option of leaving out the multiplication symbol entirely, as the examples up to now have shown.
Example: Type " 3x + 4x ".
Maple will insert a space to indicate the implicit multiplication.
In general, you can use * or a space to denote multiplication. When using standard math notation, the * appears as a center dot ( ).
Example: Type " 3 [space] x + 5 * x".
Implicit multiplication offers convenience and additional typesetting options, but if you use spaces for multiplication, be careful.
" x y " means "x times y", but " xy " means the
variable whose name is "xy".
Example: Type "x [space] y + xy ".
The result is not because the two expressions are not the same. If you choose to Differentiate using the context panel, you will see that x, y, and xy all appear as variables in this expression.
Mathematical Notation
Maple understands familiar mathematical notation.
For example, Maple understands that is a differential equation in .
Example: Enter the equation listed above (using the single quote key for the prime notation). To verify that it is in fact a differential equation, select Solve DE from the context panel.
solve DE
Label References
Maple uses label references.
Whenever you use [ENTER] to get a response, the result is automatically given a label reference. To refer to a previous result in a computation, use [Ctrl]+[L] and enter the label reference number.
Example: Multiply the result (from
above) by x^2 , using labels. Your label number
may be different than the one shown.
Adding Text
You can include text throughout your Maple document.
Steps Results
Your document can contain math, text, and nonexecutable math, which is math that you don't want Maple to evaluate because it's part of your explanation, not a calculation, You can press [F5] to cycle between modes, or use the buttons in the toolbar:
These buttons also show you which mode you are currently in.
Press [F5] to change from math input to text input, and start typing text. Try typing the start of the sentence on the right.
In Worksheet mode: Create a text region by pressing the [T] button on the toolbar, or choosing Insert > Text from the menu. Once in a text region, you can add math to your text using [F5] or the buttons on the toolbar.
The solution can be expressed as
You can combine text and math in the same line. Place your cursor at the end of your sentence, and press [F5] again to move to nonexecutable math input. Once you have entered your mathematical expression, press [F5] again twice to return to text. Using nonexecutable math in your text instead of live math is especially important if you want to be able to execute your worksheet using the Excecute All button.. If the math is live, Maple will execute the expression and show the results at the end of the paragraph.
The solution can be expressed as , so it's easily found.
You can include live calculations inside your paragraph by using live, executable math in combination with inline evaluation or context menu operations (Document mode only). You can even replace the = sign or context menu descriptions with text. Enter the example to the right, using the Factor context menu. This time, press [F5] twice so that you move from text to math mode.
Now delete the equal sign, switch to text mode, and add the replacement text.
We know that factor=^2 , so...
We know that can be rewritten
as 2 , so...
Change the +1 to -15, highlight the entire sentence and click execute all selected groups ( ) to re-execute the computation.
We know that can be rewritten
as , so...
Tip: If you are trying to enter math but it doesn't seem to be formatting properly, you are most likely in text mode. If the math looks right but it doesn't seem to get executed, you are probably in nonexecutable math mode. In live math mode, the cursor is slanted, and has a blue box around it. In nonexecutable math mode, the cursor is slanted and has a gray box. In text mode, the cursor appears as a vertical bar. Remember you can always use the toolbar to check, and change, your mode:
Tip for Worksheet mode: If the cursor is at an input prompt, [F5] will toggle your input mode between math notation and Maple syntax, for example, int(exp(x)/2, x) instead of
.
Combining Plots
You can easily add another plot on the same set of axes.
Example: Plot. Then enter another equation in x into your worksheet (e.g.
), highlight the new expression with
your mouse, hold down the [Ctrl] key and drag it onto the plot.
Annotating Plots
You can add additional information to plots by using the drawing tools. Lines, arrows, text, 2-D math, and shapes are available.
Example: Click on the plot, then select Drawing from the drop-down menu on the
left side of the toolbar:. Use the
Text Tool (T) to enter labels for the curves. Use [F5] to toggle between text and math, and standard Maple math editor entry keystrokes.
When you are finished, select Plot from the drop-down menu to exit Drawing mode.
3-D Plots
Example: Enter an expression in x and y (e. g. ). Select Plots > 3-D Plots > x, y from the context panel.
Example: To rotate the plot: Click on the plot, and then hold down the left mouse button and move the mouse.
Example: Pan and zoom the plot by selecting the appropriate tool from the toolbar or the Manipulator list on the context panel. Now when you hold down and move the mouse, the new action is performed.
Plot Options
You can modify the look of your plot in a variety of ways.
Plot options can be changed using the context panel. The available options depend on the type of plot.
Example: Click Transparency and modify the plot transparency.
Using Plotting Commands
The most commonly used plot commands are plot(), for 2-D plots, and plot3d().
Plot using the plot command as shown.
Note that you can still use the context menus to change the properties of this plot.
Plot commands take many different customization options. For example, the 3-D plot from the previous example could also be created using the command on the right.
Enter "Plotting Guide" in the search box
on the toolbar and select the Plotting
Guide. This guide is a good place to go
when you want to create something
other than a regular 2-D or 3-D graph.
More information on using commands and the help system can be found later in this document.
Snippet from Plotting Guide:
Assistants, Tutors, and Math Apps
In addition to the Plot Builder, Maple includes many other interactive tools for performing simple and complex tasks, as well as for exploring concepts. Some examples are below. See the Tools menu for the full list.
Steps Results
Using the Exploration Assistant
The Exploration Assistant allows you to instantly create interactive mini-applications used to explore the parameters of an expression, even if that expression involves Maple commands. Explore generates a user interface with interactive sliders, dials or gauges that can vary the values for the parameters and show the results.
Example: Type but don't press [ENTER]. Select Explore from the context panel. From here, you can set the range of values you want to explore, as well as specify any variables to skip. When you select skip , that parameter remains as a symbolic unknown in the expression; no slider will be created to control that value. With this expression, choose to skip x and y. Move the sliders to change the plot.
The Explore functionality is also available through the Explore() command, which provides even more functionality and customization options.
