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HEMSyM

### Help Eradicate Meaningless Symbolic Manipulation

Unfortunately, much of what we teach in "Calculus" and other courses
is meaningless symbolic manipulation. There are many reasons for this:

- inertia. This is the way we learned, so this is the way I'm going to teach.
- It is easy to test
- It gives the students a feeling of accomplishment -- "I can differentiate
50 functions in 5 minutes!"
- All the books do it. (This is because, with few exceptions -- see below --
they copy from one another.)
- It is easy to teach, just turn off your mind and start calculating on the blackboard.
- It requires no outside knowledge of the physical sciences and enginering.
- Want to add one? EMAIL me at:
morley@math.gatech.edu

Some calculus books are different. There was a batch of calculus
books in the 60s and 70s that are very good, extremely rigorous books.
Examples include Spivak's ** Calculus **, Spivak's
** Calculus on Manifolds**, Apostle's ** Calculus
**, and the famous Norman, Spencer and Steenrod **
Advanced Calculus **.
The old calculus book by **Toeplitz ** is
one of the best ever written. It is also very short. **Cauchy's **
calculus
book is great. Euler's volumes on precalculus -- **
Introduction to the Analysis of the Infinite ** have never
been surpassed. Unfortunately they fit into no standard modern course

Several calculus books are different because they are consitantly
written by people that know and understand the engineering applications
of Mathematics. The best of these is Gil Strang's ** Calculus **.

Finally there are calculus books that have really taken the computer revolution
seriously, and have thought very carefully about what it all means. Most
of the "Computer Calculus" books are compleate junk. The best are
superb.
IMHO the best of the bunch is
Calculus and Mathematica by Brown, Davis, Porta and Uhl.

There is, of course the famous ** Harvard Calculus **
project, by several well known and fine authors.
While this is certainly in the right dirrection, the book
is clearly not intended to be used at Engineering intitutes.
I actually rather like much of the Harvard calculus, but I don't
know of more than one or two of my colleges in Mathematics at Tech
that would agree with me.

In may ways, the First Calculus Book ** Analyse des infiniment petits
pour l'intellegence des lignes courbes ** by
Guillaume Francois Antoine Marquis de L'Hopital is one of the best.
(There is some controvery as to who the author was, see
here for Johann Bernoulli's side of the story. )

Return to Tom Morley's Home Page

### To get a hold of me:

Phone: (404) 894-9233, (404) 894-2700, (404) 894-4409 (FAX)
email:
morley@math.gatech.edu

Or
morley@bmtc.mindspring.com

### Y'all come back now, 'ya hear?