My Belief Statement

My Belief Statement: _It is better to be defeated on principle than to win on lies._ Arthur Calwell

Many students have a serious phobia when it comes to Math class, let alone writing an exam in that subject. I believe this phobia can be dispelled by "digging" into the "WHY " and the "HOW". In fact, many students WANT this. I attempt, wherever possible, to connect a geometric representation to its algebraic counterpart; an analysis of how the two versions interact is important. Contrary to what SOME individuals may think, I'm not at all afraid of technology. I AM, however, cautious to not "jump into the deep end"; we need to grow with this and "dovetail" the old with the new so that they COMPLIMENT each other.

I have several links in the sidebar at the right, as well as some of my own discriptions on various topics. These will grow in number and evolve over time, as will my hand-written notes; these can be viewed by following appropriate links which you will find throughout this blog. These notes will also be posted on my facebook site if that happens to be your preferred mode of viewing; I've included a link to that in the sidebar as well.

Integration - Circle Area & Arc Length

The notes contained in the link directly below show the derivation of circle area using some of the integration techniques illustrated earlier; the formula for arc length is also derived, with reference to the Mean Value Theorem.  This formula is applied to several functions to determine arc length over a given interval and is ultimately used to prove the formula for circumference of a circle.  This circumference formula is then used to once again prove the formula for area of circles, this time using the "shell" method of integration.

Circle Area & Arc Length - Samuelson

The links below reinforce the ideas presented in my notes and provide much more information on those topics.
Arc Length
Arc Length - Riemann Sum
Parametric Equation
Mean Value Theorem - Interactive
Arc Length, Area, and the Arcsine Function