1. The symbol := is used to assign a variable an expression or a value. Once this is done, the variable will retain the value or expression until it is reset. It can been seen in the Variable Palette. 

The = symbol is used when setting up equations. It is also used to temporarility assign a variable a value. Once the computation that uses that varaible is complete, no trace of the variable and its value remain in Maple memory. It is never stored in the Variable Palette. 

 

2. An 'exact' value may be something like sqrt(2); or exp(1); . An approximation is a truncated decimal represenation that comes close to the actual value of the 'exact' value. Most common is using  

3.14 for π, 2.71828 for e and 1.4142 for sqrt(2); .  

 

3. The symbol π can be entered from the Common Symbols on the Expression Palette or it can be entered on the command line as pi for the symbol and Pi for the value. e can be entered as exp(). The square root symbol is sqrt() and absolute value is abs(). 

 

4. Mutliplciation will fail if a multiplication symbol is not used between distinct variables and factors. 

 

5. The assume command, in the case of logarithms, tells Maple that the input values are positive. This is done because the domain of a logarithmic function is positive numbers. See #6 in the Math Problem Set to see the application. 

 

6. The command trigsubs() inserted a valid trignometric identity into an expression. It will fail if the trigonmetric identity provided is false. The algsubs() command will tell Maple to insert any equation into another to make a substitutuion.  It will substitue in a value or an expresssion into another expression. It simplifies.  The subs() works similarly, as it will substitute a value or a variable. It will does not insert an epxression into another expresssion.   

 

7. To clear an variable assignment, use unassignment quotes, use the command unassign( ) or right click the variable in the Variables Palette and choose unassign. 

 

8. The command simplify() attempts to take a long expression and reduce it down as much as possible. This command comes with additional arguments such as trig or ln to help inform Maple the type of function components need to be managed.  The command collect() organizes coefficients by powers on the independent varaibles.  Applying this command may result in output that appears to be partially factored. The command combine() groups terms together by operations. For example if two factors have a square root in common, then combine() puts the factors under one square root symbol. Additionally, combine() can be used to combine exponents for a common base. It can even be applied to groups of like commands.