Educational Materials

Introduction to Mathematica for High School Math (for Students and Teachers) #3

Ruth Dover

Author

Ruth Dover

Title

Introduction to Mathematica for High School Math (for Students and Teachers) #3

Description

Introduction to Mathematica for High School Math

Tutorial 3: Define

R. Dover, IMSA

Defining Variables

Defining a variable should be about as you would expect. Define both

and

, using a semicolon to separate two inputs within one line. With the semicolon at the end, no output is shown:

a=4;b=2;

3a+

Want to know if

a=b

? This requires a double equal sign:

ab

Or if

is equal to itself?

aa

But now we will redefine the value of

(this overwrites the old value, but it is better practice to clear the old value first):

b=5

Short memory? Or not sure if a value is still in Mathematica's® memory? Just ask:

Clear[a,b]

Defining Functions

To define a function, the Wolfram Language™ has some special notation using an underscore and a colon. (There is no space between

and

.) This is to show a "delayed assignment." That is, Mathematica reads the rule, but only evaluates the function when asked to do so. Watch the notation carefully!

f[x_]:=

+5x-2

After defining the function, evaluation works as expected—with square brackets:

f[3]

f[5]+f[-2]

Define a value for

and then evaluate the following:

+1]

f[2+3]

f[f[f[x]]]

Define a new function

and evaluate it with several values and expressions.

When finished, clear both

and

Clear[f,g,a]

Substituting

You may also substitute numbers or variables into expressions. First, create an expression and call it "poly." (Note the space between the

and

in the middle term. The space indicates multiplication of the two variables

and

as opposed to a single variable named

, similar to our name

poly

, which is one variable with a four-letter name. Spaces are frequently used in the Wolfram Language simply to help make the mathematical expressions easier to read. In this case, it is necessary.):

poly=

+4xy+5

To make a substitution, we use the not-so-obvious notation

along with an arrow (from the palette or created by a "–" and a ">"):

poly/.x2

Now substitute

y=5

into this poly. Mathematica does not store these values of

and

To substitute

x=3

and

y=−1

simultaneously, we can use curly braces to create a list of values:

poly/.{x3,y-1}

Now substitute

x=a

and

y=b

simultaneously.

Then substitute

for

and

−2y

for

When we have finished using poly, it is important to clear it from Mathematica's memory. You may wish to reuse the name later. Also, you do not want the program to assume something you had forgotten about. (This happens particularly with function names.

happens to be a very popular choice!):

Clear[poly]

Cite this as: Ruth Dover, "Introduction to Mathematica for High School Math (for Students and Teachers) #3" from the Notebook Archive (2021), https://notebookarchive.org/2021-09-6h1x6h6