Idiots Guide To Calculus

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Can anyone recommend some further reading for me in advanced mathematics?

I'm thinking of taking an open university course in Natural Sciences. This course will encompass everything to do with scientific study including physics, biology, chemistry, geology, astronomy etc. In my second and third year, I'll be able to specialise my study into one of the above areas. At the moment I am thinking of astronomy.

There are no prerequisites that I need to adhere to before I can go on the course, they are accepting anybody who is fairly competent at mathematics and science.

I think that it would be advantageous for me to do some extra reading on my maths since I haven't done it for so long. Can any one recommend some further reading that I can do to help brush up on my maths??

In particular I need geometry, calculus and linear algebra. Preferably an idiots guide to this subjects since two of them I have never encountered before?

Hope you can help.

www.khanacademy.org

It's gotten a lot of high praises for quality. I'm working my way through it myself for a similar purpose as yours, i.e. I need to refresh my memory on all the mathematics classes I've had before taking on something more serious.

Idiot's Guide to Calculus AGD


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Idiots Guide To Calculus

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Differential Equation: decomposition of radium?

The radium in a piece of lead decomposes at a rate which is proportional to the amount present. If 10 percent of the radium decomposes in 200 years, what percent of the original amount of radium will be present in a piece of lead after 1000 years? Please solve by incorporating in the following formula: dx/x = -kt. Answer:59.05 percent.

- hmm, why isn't he providing any kind of work? - Well, I'm trying to teach myself coming from an Idiot's guide to Calculus which I just completed and am now trying ODEs when I found this being the very first question. Do I let x = 10% and k = years?

dR/dt = aR (first statement)

"try" (I know answer) R = Ro e-kt

dR/dt = -kRo e-kt = -kR yep a = -k

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R(200) = .9 Ro = Ro e(-k200)

.9 = e(-k200)
ln(.9) = -k 200
k = -ln(.9)/200

plug and chug; you now have k

% remaining after 1000 years is

100 * e(-k1000)

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another way to get it is you knock down to .9 after 200 years and you do that 5 times

(.9)^5 = 0.59049 ; yep agrees with prof

Idiot's Guide to Calculus AGD 2


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