- Introduction
- Assigning labels
- Entering an expression
- Entering a function
- Evaluating functions and expressions
- Plotting
- Exercises

> myname := 1.5;Once you hit return after this Maple line, any time the string of characters

> myname; > myname := 'myname'; > myname;Once you have cleared the variable, you are free to use it again. Another thing to keep in mind is that if you close your Maple worksheet for any reason and reopen it, none of the commands will be stored in memory until you re-execute each command by hitting return after each of the Maple lines. This can also be done by clicking on the

> expr1 := x^3+3*x^2-x+1;Note that in the expression above, there is an asterisk between 3 and . A common mistake is to write two functions next to each other without the "*" symbol. This would give incorrect results when using this expression since Maple doesn't understand implied multiplication.

> f := x-> x^3+3*x^2-x+1;Below is how ``NOT'' to enter a function:

> f(x) := x^3+3*x^2-x+1;The difference between expressions and functions are first the obvious, that expressions do not have to satisfy the definition of a function in the sense that for each number in the domain, there is a unique number in the range. A function may be defined as an expression, but not all expressions can be defined as functions. The differences in Maple are numerous as you will see below when we evaluate the expression or function for a given value and when we use the

> subs(x=2,expr1); > subs(x=2.,expr1);In the

> subs(x=a+h,expr1); > subs(theta=Pi,sin(theta)*cos(theta));In Maple, functions are much easier to evaluate than expressions. In order to evaluate the function at , then simply type

> f(2);Here are a few more examples of evaluating functions.

> f(a+h); > f(Pi); > evalf(f(Pi));Note the use of the

> evalf(Pi,100);

> f := x-> x^2; > plot(f(x),x=-2..2);The

> plot(x^2,x=-2..2,y=-5..5,title=`My First Plot`);This particular command allows you to add arguments, but if you were to leave off one of the essential arguments, you will get an error message. You can also plot more than one function or expression on the same graph by enclosing them in curly braces ``{}'' and separating them by commas. For example, we can plot and on the same graph.

> f := x-> x^2-2; > g := x-> -x+2; > plot({f(x),g(x)},x=-4..4);

- Enter
as an expression
and choose a variable name of your choice.
- Evaluate this expression at .
- Evaluate this expression at and give your answer in decimal form.
- Evaluate this expression at .
- Plot this expression over the range .

- Repeat exercise 1 by first defining as a function.
- Define and as functions. Plot them both on the same graph. Estimate the two intersection points by observing the plot. Plug each value back into both functions to show that the values are the same.

2002-10-29