PreCalculus
Precalculus is all about understanding functions, and as such, requires a fair amount of graphing. This page will focus on the needs of students in a Precalculus course, getting started with installation, learning to use Maple, and will have examples of commands and graphing techniques. All the pages are found by hovering over the tabs above to see the drop-down menus or from the list in the column to the right
Module 00: The first thing you need to do is to install the software from the DVD, so go to the How To Install Maple page. After the software is installed and activated, you need to check out some of the tutorials. I recommend the Getting-Started page, which links you to Maplesoft’s video training, Quick Reference cards, and more.
Module 01: You will need to use functions, so it’s important to be able to create one, evaluate, and plot. Here is a little information on how to Enter a Function. You will also need to be able to Plot a Function. Additional examples can be found in the Plotting Examples page (part of the Tutorial Collection). Another skill is using the expressions palette and / or finding the Maple command. There are examples in the Expressions Palette page. Specifically, you need the square-root function and the absolute value function. Both of these are found in the expressions palette, or one can use Maple function commands sqrt(x) and abs(x).
Module 02: It is important to keep in mind that with higher order polynomials, you may need to rescale the vertical axis in order to see important functional behavior. The default x-axis range is from -10 to 10, but the y-axis range is based on the the evaluation of the function across the range of x. Here is a link to an example of rescaling the axes.
Typing in rational functions is best done by typing the numerator, then selecting the numerator before entering the “/”, OR you can place parentheses around the numerator.
Module 04: Working with trigonometric functions is similar to other special functions. It is important to use the parentheses for the angle. For example: use sin(x), cos(3*x), tan(theta), csc(Pi/4), sec(a+b), cot(x+Pi/3). Since the standard period of these function is a multiple of Pi, Maple (version 16 and above) graphs the function with the horizontal axis subdivided based on fractions and multiples of Pi. It is important to use capital P, lowercase i (Pi), or to use the Greek letter for pi from the Common Symbols palette. Angles are in radians.
Inverse trigonometric functions: commonly used are arcsin(x), arcos(x), arctan(x). These value of x is expected to be a real number and the function returns the angle in radians in the range of the function. It is up to the user to determine what quadrant the angle is actually in to determine the complete answer.
Module 05: There are a number of new skills needed.
M05x: Working with Polar Plots requires the use of the plot[polarplot]command (typing ?polarplot as a command in Maple will take you to the Help page). Here are several simple examples:
M05z: Working with matrices generally falls under the topic of Linear Algebra. There is a tutorial on entering and using matrices and on common matrix operations. Link to Working with Matrices.
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