Steps

Results

Using [Enter]

When you launch Maple you start with a blank document, with menus and toolbars at the top and palettes on the side. At the cursor, you can start typing math. Press [Enter] to see the result.

Example: Type "1+2 [Enter]".
Notice that the result appears on the next line.

Example: Type "x^2 +5 -2".  Notice that typing "^" automatically moves you to the exponent position. To leave the exponent, use the right arrow [→] key.  Press [Enter] to see the result.

Context Menus

You can use Maple's context-sensitive menus to perform a wide variety of mathematical and other operations.  

Example: Place your cursor on the last result, and right-click. The context-sensitive menu offers several operations that you can perform on the current expression.  To integrate this expression, select Integrate, then x.

Example: To plot the result of the integration, right-click on the result, and then select Plots > 2-D Plot.

Tip: You can modify the plot after it has been created.  Simply click on the plot and then right-click on the plot and use the context-sensitive menus, or access the Plot menu and the plotting toolbar.

Changing the Problem

Mathematics in a Maple document are live. You can go back, make changes, and re-execute the problem to obtain a new result.

Example:  Go back to your original calculation "", change the number "1" to a "3", and press [Enter]. Note the change in output.

Example:  In the context menu example, above, change the  to .  Highlight the entire line, including the plot, then click the execute button, , found at the top of the Maple worksheet. All selected calculations are updated.

Steps

Result

Exact Answers and Numeric Approximations

Maple calculates exact answers. That is, fractions remain as fractions and  and  remain symbolic throughout calculations.  This reduces errors due to approximations in multi-step calculations.

Example: On a new line, enter "1/2 + 1/3".

Note that typing [/] automatically moves you to the denominator. The right arrow will take you out.  Press [Enter] to see the result.

Maple also calculates numeric approximations.  

Example: Right-click the above result and select Approximate from the context menu. Select accuracy of 5 digits.

If your problem uses decimals already, Maple will return the answer in the same format, with floating point numbers.

Example: Enter , and press [Enter].

You can apply different formatting to numeric results.

Example: Right-click the above result and select Numeric Formatting... from the context menu. Select Scientific, then press Apply Formatting.

Palettes

Maple has over 1000 palette symbols within more than 20 palettes.  You can use Maple's Expression palette to enter common mathematics expressions.  This palette contains fill-in-the-blank templates for common operations.

Example: Using the Expression palette, find the integral of .

Start by placing your cursor where you want to work.  Open the expression palette (click on Expression on the left-hand side of your Maple document) and click the indefinite integral .  An indefinite integral template will appear in your worksheet.  Fill in the placeholders, using [Tab] to move to the next placeholder. When done, press [Enter] to evaluate.

Example: Use the expression palette to find the limit of a function.

Start by placing your cursor where you want to work.  Open the expression palette (click on Expression on the left-hand side of your Maple document) and click the limit expression  . Fill in the placeholders, using [Tab] to move to the next placeholder. When done, press [Enter] to evaluate.

Tip: Put frequently used palette entries on the Favorites Palette. Right-click on the palette button and select Add to Favorites Palette.

Symbol and Command Completion

The symbol and command completion mechanism provides an alternative to palettes for entering symbols.

Type the first few characters of the symbol name, and press [Esc]. Choose the symbol you want from the list.

Example: Try entering  

To enter type "pi [Esc]".  Select the symbol

Use [^] to enter the exponent.  To leave the exponent, use the right arrow [→] key.

For , enter "sqrt [Esc]".Select the   option. Press [Enter].

To enter the exponential function  or the imaginary number , use symbol completion.

Example: Plot .  Use symbol completion to create the exponential .  Type "e [Esc]", and select e (exponential) from the list.  Then use the context menu to plot the function, by selecting Plots > 2-D Plot of Right Side.

Note: Simply typing "e" will produce the name e.  To enter the exponential function, you must select e(exponential) from the symbol completion list.  Alternatively, you can use the  template from the Expression palette.

Some command completion templates offer calling sequences for Maple commands, making it easy for you to get the syntax right on your first try.

Example:  Find the taylor series expansion of  about the point 2.

Type "taylor [Esc]".  From the list, choose taylor(series expansion).  The template  is entered into your document.

Simply replace  by ,  by , and  by 2.  The last parameter, , is the order of the expansion.  We will find the 4th order expansion.

Case-Sensitivity

Maple is case-sensitive.
 
Example: Compute .  Compute .

Compare the results.

Implicit Multiplication

Maple understands implicit multiplication. A space between terms is understood to mean multiplication.   

Example: Type "3 [Space] x  [Space] y"for "3 times  times ".

In the case of a number times a variable, the space can be omitted.

Example: Type "3x [Space] y"for "3 times  times ".

For readability, Maple automatically formats the expression to include a space between terms.

Caution:  The space can only be omitted in the case of a number multiplied by a variable. All other cases require a space or an explicit multiplication symbol (*).  

For example, "" means " times ", but "" means the variable whose name is "".

Example: Type " [Space]  ".

If you choose to Differentiate using the context menu, you will see that , , and  are treated as three separate variables due to the way they were entered.

Avoid confusion with function calls.  To us,   looks like a function call, and  looks like implied multiplication.  Maple understands both of these as function calls. You must use a space or an explicit multiplication symbol to denote multiplication.

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 menu.

Label References

Maple uses label references.

Whenever you use [Enter] to get a response, the result is automatically given an equation label.  To refer to a previous result in a computation, use [Ctrl][L] and enter the number of the equation label.

Example: Multiply the result  (from above) by , using labels.

Assignments

After entering an expression or performing a computation, you can assign the result to a name.

Example:

Enter the expression to the right, right click on the output and select Expand.

Right-click on the output  and from the context menu choose Assign to a Name.  Enter "Answer1".

You can then use this name to refer to the result and to use it in further computations.

The assignment statement := (colon equals) assigns the right hand side to the name on the left hand side.

Example: Assign values to "value1" and "value2" and then add them together.

Sometimes you do not want to see the results of the assignment statement. To suppress the result of any Maple operation, end your statement with a colon (:)

Example: Assign a value to , but do not show the result. Then, compute .  (To get a subscript, use the underscore key [_].  Use the right arrow to leave  the subscript.)

To clear a variable, use the unassign command. You must enclose the name in right single quotes [''].  This prevents Maple from automatically replacing with its value before passing it to the command.

Note:  In Maple, you have to execute a command before it is processed.  Thus, you must press [Enter] (or [Ctrl][=] to display the result inline; for more information see 2-PuttingYourIdeasTogether) after each statement.

Maple Commands

You can always enter Maple commands by typing them directly. Examples of Maple commands will be found throughout the tutorials.

Example: For instance, the definite integral of  can be expressed using the integral symbol from the palettes or using the command int.

The calling sequence for definite integration is int(expression,x=a..b), where a and b are the endpoints of integration.  A range in Maple is given by a..b.  

You can enter the exponential function using symbol completion or using the name of the Maple command.  The name of the Maple command for the exponential function  is exp.

Type "int(exp(x^2), x = 2.1..2.4)".

Example: Earlier, we solved the differential equation  using the context menu.  Now, we will solve this using a command.  dsolve is the differential equations solver in Maple.  

Solve the differential equation above using dsolve.