Reinventing the wheel -- links to Calculus Websites

Two very promising looking calculus sites, I will study them before going on too much on my own account....

A Gentle introduction to learning calculus:

http://betterexplained.com/articles/a-gentle-introduction-to-learning-calculus/


Calculus.org - lots of links

http://www.calculus.org/

Maths problems: Take two

Math problems: Basic Technical Mathematics with Calculus 5th Ed
Ch 1. Exercise 1-13
Q3. Three meshed spur gears have a total of 107 teeth. If the second gear has 13 more cogs than the first and the third has 15 more than the second, how many gears have each?

Preamble -- I'm assuming this is another set of simultaneous equations
( this is more of a scratch pad than an explanation, hopefully previous take will give general idea)
Three unknowns, totalling 107
a + b + c = 107
second is 13 more than first
b = a + 13
third is 15 more than second
c = b + 15
we can substitute in stages:
a + b + (b + 15) = 107
a + (a + 13) + (b + 15) = 107
a + (a + 13) + ((a + 13)) + 15) = 107

quick check: 13 + 13 + 15 = 41

a + a + a + 13 + 13 + 15 = 107

3a + 41 = 107
3a = 107 -41
3a = 66
a = 66 / 3
a = 22
b = a + 13 = 35
c = b + 15 = 50
22 + 35 + 50 = 107
3a = 107 - 41
3a = 66
a = 66 /3 = 22
b = a + 13 = 35
c = b + 15 = 50
22 + 35 + 50 = 107

Android SDK

I finally got it to work. Sheesh. A bit rough around the edges

Maths Problems: Take One

Math problems: Basic Technical Mathematics with Calculus 5th Ed
Ch 1. Exercise 1-13

Q1. Two computers programs cost $390 dollars together.
If one costs $114 more than the other, what is the cost of each?

I was going to jump ahead on this one,
but I couldnt quite figure it out.
Anyway -- the statement of the problem gives us our hint

Two computer programs ...
we have two unknown numbers
so lets call them
a and b
a + b = 390
one costs $114 more than the other

a + 114 = b
or
b = a + 114
since b = a + 114 then we can replace b with a + 114

so we now have:
a + a + 114 = 390
which is the same as
2a + 114 = 390
we can move the 114 across to the right hand side of the equals and subtract it:
2a = 390 - 114
2a = 276
we can move the 2 across and divide it off 276
a = 276 / 2
so we can now calculate a:
a = 138
and we can get b because we know
b = a + 114
b = 252
so we can double check
a = 138
b = 252
-------
a + b = 390
138 + 252 = 390

Jump ahead

I'm jumping ahead of the book. (Basic Technical Mathematics with Calculus by Allyn J Washington 5th Ed)
So there are some risks, but the calculation is the same as the result given in the back of the book

A new departure

Originally I had all sorts of plans to cover things like retro-fitting Unit testing to the likes of VB6, which I never got round to in real life and so neither in the blog. With all the talk lately of the Science Deficit (worldwide) I had a wheeze, why not work through some Sums in real time?
Two snags: "Sums" (thats mathematics to you) is hard work to all but the uninitiated and although I got into it eventually, my insights might be of minor use and less entertainment. Still, if the struggles of somebody in their mid-forties trying to re-learn some calculus adds to the world of knowledge, I should give it a shot.
Going to try to do a few problems a week, and maybe not blog them that often, because explaining is harder than doing as always...