# On the Use of Computer Algebra Syntax in
the Calculus Classroom

## Abstract

In this talk, the idea of using computer algebra syntax in
a

calculus course will be presented. The presenter believes that

students, to a certain degree, can become acquainted with

CAS conventions and syntax before ever sitting down and

wrestling with such software.

Moreover, this intentional syntactical use might lead to

better understanding of the composition of functions, and thus

better understanding of the concepts of the Chain Rule (for

derivatives) and the Substitution Method (for antiderivatives).

The presenter will show some sample assignments as well

as discuss the pros and cons of such an idea. There will be

time for general discussion of this notion both during the

presentation time, and hopefully afterwards for any interested

parties.

## The Main Issues

• Student understanding of composition of

functions and order of operations

• The steep learning curve of Mathematica

(or any other CAS)

• Students' electronic communication of

mathematics (e.g. via email, on message

boards, etc.)

## Ideas and Implementation

• Compare /contrast mathematical notation

and computer algebra syntax

Integrate[Sin[3x],x]

• Occasional but consistent use of

Mathematica syntax in class

• Guidelines for electronic

communication of mathematics

• Any others?

## Pros and Cons

• Cons

1. The Mathematica learning curve

2. Isn't calculus hard enough already?

• Pros

1. Fewer mathematically ambiguous

emails!

2. Students are forced to think about

composition of functions

3. Math/CS majors are introduced to

conventions of a programming

language

You may spend as much time on this exam as you wish, but
once you begin working on

it, you may not consult any resources (including calculators and Russ !) until
you have

completed it. Your exam will be graded before you leave.

**Evaluate each antiderivative. SHOW ALL OF YOUR WORK!**

You may spend as much time on this exam as you wish, but
once you begin working on

it, you may not consult any resources (including calculators and Russ!) until
you have

completed it. Your exam will be graded before you leave.

**Evaluate each antiderivative. SHOW ALL OF YOUR WORK!**

1. Integrate[(3-8x)^11,x]

2. Integrate[(t^3-3t+1)/t,t]

3. Integrate[x*Sin[x],x]

4. Integrate[x^2+5/Sqrt[x],{x,1,3}]

5. Integrate[Exp[3x],{x,-Infinity,0}]

## Guidelines for Mathematical Emails

In this course, I strongly encourage you to come to my
office hours for help with

homework or preparation for exams. However, the use of email as a form of

communication is also encouraged. The following is a list of “translations” of

mathematical notation into pure text format. I would encourage everyone to
become

familiar with these conventions and to use them in any mathematical email

correspondence with me.

-----Original Message-----

From: Andrew C Hartwig

Sent: Wednesday, February 12, 2003 5:10 PM

To: Russell Goodman

Subject: RE: YO Questions

Prof G

Can I legally move the five out front with

this expression

u^5 * ln 5u to

5 integral u^5 * ln u

Andy

-----Original Message-----

From: Russell Goodman

Sent: Fri 10/11/2002 8:38 AM

To: Sundance Visser

Subject: RE: calculus

Sunny:

***SNIP***

On #16, substitution does work. Let w = 5u,

so that dw = 5du AND u = (1/5)w. The

integral then becomes:

Integrate[(w/5)^5* Log [w]*(1/5),w]

=Integrate[(w^5/5^5)*(1/5)*Log[w],w]

=Integrate[(w^5/5^6)*Log[w],w]

=(1/5^6)*Integrate[w^5*Log[w],w]

It's a bit ugly, but I hope that helps!!

From: Russell Goodman

Sent: Tuesday, October 08, 2002 10:52 AM

To: Brady E Kurtz

Subject: RE: 7.2 homework questions

***SNIP***

Anyway... The derivative of (Log[t])^2

requires the Chain Rule:

D[Log[t]^2,t] = 2Log[t]*(1/t)

Now, if you meant problem #35 ( like others

have asked about), use the hint:

D[ArcSin[u^2],u] = 2u/Sqrt[1-u^4], where

Sqrt means square root .

***SNIP***

From: Russell Goodman

Sent: Wednesday, March 19, 2003 2:30 PM

Subject: [Calc 2] Mathematica Help

I realized a few minutes ago that

Mathematica's " Solve " command doesn't work

too well when using functions like Cosh[x],

so here's an alternative, if you need it.

If I were trying to solve the equation

15Cosh[45/x]-x^2=0, I would want to use the

following Mathematica command, called

"FindRoot":

FindRoot[15Cosh[45/x]-x^2 == 0, {x,20}]

The {x,20} part just tells Mathematica what

variable you 're using and it also gives it a

"starting x- value " to try, just like the

"Guess" that the TI-83 asks you for when

doing certain things. I just guessed x=20

to start off with.