Introduction to Mathematica for High School Math (for Students and Teachers) #1
Author
Ruth Dover
Title
Introduction to Mathematica for High School Math (for Students and Teachers) #1
Description
Introduction to Mathematica for High School Math
Category
Educational Materials
Keywords
Mathematics, education
URL
http://www.notebookarchive.org/2021-09-6h1k3vw/
DOI
https://notebookarchive.org/2021-09-6h1k3vw
Date Added
2021-09-14
Date Last Modified
2021-09-14
File Size
23.2 kilobytes
Supplements
Rights
Redistribution rights reserved
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Tutorial 1: Getting Started
Tutorial 1: Getting Started
Ruth Dover
Illinois Mathematics and Science Academy, Emeritus
Illinois Mathematics and Science Academy, Emeritus
You have just opened a Mathematica® "notebook." It is a ".nb" file. This one is designed to give an introduction to some of the many features of Mathematica—the mathematics as well as the workings of the program. Many of these ideas will be seen again in more detail in later notebooks. Each notebook has a primary topic, but smaller topics are also included, so the notebooks should generally be done in order.
This set of tutorials is geared toward pre-calculus and calculus students and teachers. If you are in pre-calculus, just ignore the calculus examples!
What you see now is similar to an outline form, with section headings shown. Following this paragraph, find the line with "Numbers" in orange. "Numbers" is a "section" heading. We want to open this section, and there are two ways to do that. The easiest is to click the to the right of the word. Clicking again will close the section. Alternatively, move the cursor to the far right of that line to the vertical bar with the little triangle at the bottom. The cursor will change to a vertical segment with an arrow. Double-click this bar with the triangle to open the section. Try opening and closing the section a couple of times. Then follow the directions within the section.
Numbers
Numbers
Find the line following with in a different font. Move the cursor to this "input line" so that the cursor appears as a vertical I-bar and click. Then press Shift+Return (Mac) or Shift+Enter (Windows) (a simple Return only moves the cursor to the next line, just as it does in a word processor):
20
20
OK, so Mathematica can simplify. Also, if that was not effectively instantaneous, that is because another program called the "Mathematica kernel" has to be loaded the first time. We can try another one (again, press Shift+Enter or Enter to execute the command):
10
Well… that was exciting. The number is exact, so Mathematica left it alone. We can make a slight change. Again, put the cursor in the following line and execute the "input cell." (A "cell" may be just about anything—a command, text or a section header such as "Numbers." "Input cells" are recognizable by the different font and may be "executed." Each cell is shown individually and in groups by the brackets to the far right.):
N[
10
]At least it did something. How about a few more decimal places? Edit the previous line so it reads: by typing "" after the square root but before the closing bracket. (Do not type the quotation marks!) Execute the cell. What happened? Then execute the following cell. Note the different expression for the square root:
N[
20
,50],50
Sqrt[48]
Again, at least it simplifies, but we will ask for a numerical approximation. We could do this by editing the previous cell, but we will learn another method here. Create a new cell by moving the cursor below this paragraph so that the cursor changes to a horizontal I-bar. Click. A horizontal line should appear. Then start typing: and Mathematica will make room for you. Note that the refers to the last output chronologically. Using "Ins" and "Outs" that are created by Mathematica allows you to refer to previous work as well.
N[%]
%
We will try a couple of other things. Sine and tangent are built-in functions. As such, they must be capitalized, and their arguments are in square brackets. Execute each of the two cells following. Find numerical approximations. Or edit the expressions (create your own if you wish, but we will come back to that later):
Sin+Tan
π
3
5π
6
100
∑
k=1
1
2
k
Symbolics
Symbolics
Execute each of the following cells to see a bit of simplification:
3-6+5+4-3
4
x
2
x
2
x
Simplify[(4+5+3)-3(2-6x+1)]
3
x
2
x
2
x
8
(3x+2y)
That last one may not have been what you expected—or desired. Mathematica simplifies automatically, but it will not expand, since that form will not usually be considered simplified. Tell it to expand:
Expand[]
8
(3x+2y)
Create a new cell below this one to "Factor" the last result. (Remember that the command must be capitalized and square brackets are necessary. Use % to refer to the last output in expanded form.)
Now we can take a look at a few more commands. Consider the fraction -3x+2. First, enter it by executing the cell so that it is in the computer's memory:
2-3
2
x
2
x
2-3
2
x
2
x
Now create new cells and ask Mathematica to perform each of the following commands, one by one, on the previous result: , , , and . (Use the capitalized command with the square brackets, and use % to refer to the last output. Note that ExpandAll is written with a capital "A" but no space between the words. It is one Mathematica command.) Note the coloring changes as you type. When you are in an input cell, Mathematica will change the letters from blue to black as soon as it finds a word in its vocabulary.
Apart
Together
Expand
ExpandAll
Simplify
Plots
Plots
The graphics capabilities in Mathematica are spectacular. Here is the simplest of beginnings:
Plot[(-5x+2)Sin[x],{x,-3.5,3.5}]
3
x
Plot3D[Sin[+],{x,-π,π},{y,-π,π}]
2
x
2
y
We will come back to this topic shortly.
Cite this as: Ruth Dover, "Introduction to Mathematica for High School Math (for Students and Teachers) #1" from the Notebook Archive (2021), https://notebookarchive.org/2021-09-6h1k3vw
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