Calculus I Notes, Section 1-4

Notes, Lesson 1.4
Graphing Calculators and Computers

Technology allows us to work with much more complex work than would be humanly possible, and it allows us to do work much more quickly. Relationships can be seen that would otherwise be invisible. We intend to make use of the Maple mathematics software to do explorations, simulations, graphing, and calculations to make Calculus more meaningful. We also want students to be able to see the power and use of technology as it may apply to their future work.

There are some pitfalls that can happen when using either graphing calculators or computer software. Some of them are:

1	Display windows often give an incomplete or misleading picture. The user must think domain and range to tell the software what size window to use.
2	Graphing calculators and computer software graphing tools usually try to "connect" points together. There are times when points should not be connected (for example: near an asymptote).
3	The last digit of a numerical display (usually calculator) is not accurate. Calculators usually store one digit beyond the display, and then round off the last visible digit. This makes the last digit unreliable.
4	Calculators and mathematical software always give the primary angle when solving inverse trigonometric calculations. The primary angle is not always the correct answer. In this and other situations, too much trust in a calculator or software answer can be dangerous. As always, estimation and interpretation of results in relation to the problem are necessary.

Some Guidelines for Using Maple:

#	Guideline	Example(s)	Details / Explanation
1	In PC lab load Maple using the Start button		Start/Programs/Maple V Release 4/Maple V Release 4
2	> is your prompt to enter a command		If '#' is your first character, then you may type any text for reference, and Maple does not attempt to execute a command.
3	Always follow commands with a semicolon	sin(Pi/2) ;	Note 'Pi' is understood to be.
4	Plot command used for graphing	plot(3*x+4,x=-10..10);	*Note '' is used to indicate multiplication.** Software (or calculator does not understand 3x as 3 multiplied by x)
5	If any parentheses are needed for function, then 2nd level of parentheses must be around entire function	plot([sin(x) ], x=-2Pi..2Pi);	Because the sine function requires us to put the argument in parentheses, we need to inscribe the entire function in brackets.
6	In plots it is important to choose your viewing domain and range. (viewing rectangle)	plot(x^3-2x^2+4x, x=-10..10, y = -20..15* );	Often the domain is sufficient. Maple will automatically pick the range. If a function's range is infinite you may have to specifiy a range to make the result meaningful .

Guidelines are continued in the examples for this lesson.

Check Concepts

#2: True or False: Calculators are always correct.

#3: True or False: Automated graphing systems usually try to connect points, even when they should not.

#4: (Review) To graphically check if you have a function, you should use the...

#5 True or False: With calculators and mathematical software, there is little need to learn mathematics.