It's good to put directions at the top of the problem so that when people print out the solution, they have the questions to go with them.
My new nickname for you is The Calculus Kid. I hope you keep posting and fixing up the calculus section. It had always been neglected.
Check out these changes: Calc2.3
My philosophy is that if you understand the problem and I understand the problem, we should be able to independently reach the same solution. So if you understand a problem and solution in a book, it's okay to copy it. For abstract algebra proofs, the same thing goes. Nobody's name is attributed to proving that a field is an integral domain, but if you want to copy the proof of FLT, that's different. So I suggest that you understand the proof and write it up in your own words. If the proof that you're reading is really good, there won't be any extraneous words and you might not be able to change it much. But as long as you can reproduce it yourself independently of the book, it's just a matter of listing logical statements and not copying someone else's ideas, so I think it's okay. You could put in the name if it's normally there, like "Zorn's Lemma" or "Laplace's Theorem." Of course I'm a mathematician and not a lawyer.
Nice work on the Calculus section. As a bit of advice, it's usually better to use lowercase \pi () rather than \Pi () for the constant, since the uppercase is used for something else.
I put a Multivariable link on the front page. It makes the two columns much more symmetric. -Todd
Geoff, Just follow this site's sections- it gets a lot more traffic than mine.
It looks like you've done quite a bit with the page and I must commend you. Here is a list of the "chapters" and "sections" I would think be inclusive of most single-variable calculus problems:
- Limits and Continuous Functions (no specific sections, though you might think of some big ones to add)
- Formal Definition
- Basic Rules (basic rules on power, trig and exponential functions)
- Product Rule
- Chain Rule
- Implicit Differentiation
- Logarithmic Differentiation
- Applications of Differentiation
- Interpretations (basically word problems)
- Local linearization (would include slopes and tangent lines)
- Optimization (or "Extreme Values" or some other such name)
- l'Hopital's Rule
- Mean Value Theorem (don't know how necessary this one is, it's so basic)
- Riemann Sums
- Fundamental Theorem of Calculus (including 2nd FTOC, as they're all equivalent to one another)
- Integration by Substituion
- Integration by Parts
- Trigonometric Integrals
- Trigonometric Substitutions
- Partial Fractions
- Improper Integrals
- Applications of Integration
- Interpretations (more word problems, or your section on finding the average value of a function)
- Arc Length and Surface Area
- Work and Pressure
- (Maybe one on Center of mass as well?)
- Infinite Series
- Convergence Tests
- Power Series and Intervals of Convergence
Wah! That's about it. I left out sections on Simpson's Rule and whatnot, but if you feel that to be crucial (I don't), that might be added into the Applications chapter as well. It's actually not that different from what you've already constructed, though I did get rid of the Quotient Rule and Generalized Power Rule as they are mere applications of the Chain and Product Rules. One thing that may or may not be a good idea is using alphabetical codes for each section, (like Calc.CR.1, Calc.CR.2, ... for chain rule problems) so that if new sections need to be added they could be inserted anywhere without disrupting the classification scheme. Hopefully this will be of use to you, but please let me know of any further suggestions you would have for the calculus page.
I made some changes: Calc2.51 history
I made the picture with GIMP. (It's free for linux and windows and better than photoshop). Make sure it's right. And look at the more detailed footer- since the calc page is so big now.
Check out this signature template I made- Template:Todd. And edit this to see how it works.