Introduction

Math Day Logs Index

 

Dale's Mathematics

2009 Daley Log
Page 24

Next Log Page

Wednesday December 9, 2009 Lethbridge

7:00 am

My goal today is to spend 2 hours working through the problems in Jack Weiner's book, "The Mathematics Survival Kit".

Principles for Learning calculus:

• spend 2 contiguous hours, at least 3 times a week.
• make both web site and hand-written notes (hand-written: using my Pelican fountain pen!).
• Read book. When you see an example, write out the question and see if you can do it.
• construct a table of important concepts.
• add reflective comments in a tan colored box (web site) or handwritten if the notation requires it.
• primary resource: "The Calculus Lifesaver" (2009) by Adrian Banner.
• additional resource: "Calculus Know-It-All (2009) by Stan Gibilisco.
• additional resource: "The Mathematics Survival Kit" (2005) by Jack Weiner.
• Additional resource: "Mathematica Demystified" (2009) by Jim Hoste.

 

Concept	Definition
factoring difference between squares	know formula
factoring difference between cubes	know formula

I had no difficulty with the examples for the first two chapters of the Weiner book. I am not that familiar with the term "rationalize" but I understand the idea. On the other hand the examples and exercises all seem a bit contrived. But it is good practise with symbol manipulation. I like the examples where the expression for a limit appears to be of the form 0/0. This is a good case where I would like to see the graph of the expression. This is where Mathematica can be useful. Now to recall how to use Mathematica using Parallels on the Mac. And how to save the results on this web site. This breaks down into a technical problem and then a Mathematica problem.

 

Here is the link to my handwritten work for today:

Here is the link to my Mathematica session. This is fantastic. I can now see the graphs of these functions and verify that the limit of the function as x approaches a particular value is indeed the value that I obtained algebraically. I have never been able to do this before (and other students without access to a powerful mathematics program are still not able to do this).

The technology problem turned out to be a non-problem. I simply loaded Parallels, opened Mathematica, loaded my last session (which had saved the files to a Dreamweaver folder), and then edited the session to display a few new graphs. I then saved my work as both a Mathematica file (so I could access it later) and as an HTML file (so it could be viewed on this web site).

The Mathematica problem also turned out to be quite simple. There were two "tricks". One was to remember to press shift-enter instead of enter to evaluate an expression. Fortunately I did recall this. The other was to realize that the symbol for exponentiation was ^ instead of *.

 

Books on the Go Today
	see below