Talk:Calculus/Archive 2

Pages from wikipedia

The following is a list of pages from wikipedia which contain good stuff. Could take stuff (e.g. pictures!) or simply link to some of these.

Maybe one day it would be useful to setup a system for recording when a page has been (a) linked to (b) harvested (c) has a link back to the wikibooks? Juliusross 20:39, 14 October 2005 (UTC)

Wikipedia pages

Following are taken from List_of_calculus_topics

Useful:

Wikipedia:Graph_of_a_function

Wikipedia:Secant_line

Wikipedia:Slope

Wikipedia:Stationary_point

Wikipedia:Maxima_and_minima

Wikipedia:Taylor's_theorem

Wikipedia:L'Hopital's_rule

Wikipedia:Fundamental_theorem_of_calculus

Wikipedia:Limit_of_a_sequence

Wikipedia:Natural_logarithm

Wikipedia:Exponential_function

Wikipedia:Maclaurin_series

Wikipedia:Green's_theorem

Possibly less useful (depending on scope of the book) but still worth a look:

Wikipedia:Concavity

Wikipedia:Radian

Wikipedia:Antiderivative

Wikipedia:Factorial

Wikipedia:Binomial_theorem

Wikipedia:Limit_of_a_function

Wikipedia:Newton's_method

Wikipedia:Partial_fractions_in_integration

Wikipedia:Partial_fraction

Wikipedia:Gabriel's_horn

Wikipedia:Gottfried_Leibniz

Wikipedia:Isaac_Newton

Wikipedia:Leonhard_Euler

Wikipedia:Colin_Maclaurin

Wikipedia:Brook_Taylor

Wikipedia:George_Gabriel_Stokes

Other wikipedia pages

wikipedia:Intermediate_value_theorem

wikipedia:Mean_value_theorem

wikipedia:Multiple_integral

Rolle%27s_theorem

Philosophiae_Naturalis_Principia_Mathematica

I think that is OK to take material from wikipedia as long as it appears in the acknowledgements (which it now does) juliusross

Problem Sets?

I'm taking calculus 3 from a real text book right now. The only way I can learn anything thing is through problem sets and the solution sets. Also This book needs more fully typed examples just like a real text book.

Chapter Organization

I think the current organization is not ideal. If I wanted all things involving Differentation, I would type Differentation in the search bar and click go. This would yield 5 pages of search results, so I would probably just start with the first option, Calculus:Differentation. Now that I am more knowledgeable, I would go to the Calculus:Differentation contents page, and see all the topics there, with each article listed like so: Calculus:(insert specific title here). I suggest that we change these to Calculus:Differentation/(specific title). This would require some major reformatting of all the contents pages, but I feel this would lead to easier navigation, especially for the casual reader. --SimRPGman 02:32, 9 November 2005 (UTC)

That seems a good idea. You might want to look at the naming convention on the community portal page to see what they suggest. Juliusross 15:25, 9 November 2005 (UTC)

Substitution rule

I understand the substitution rule, but there is one sitution I dont understand. Say we have f(x) whose integral is F(x). Let f(x) be for example 1/(1+x^2). Everyone knows its integral is arctan(x), but I dont undertand the method. First, they substitute x to tan(u), so that dx=sec^2du and the whole thing become 1, which has an antiderivative of u = arctan(x). But doesnt the substitution rule only apply if one changes f(x) to u? And not x to f(u)? Because the chain rule states the derivative of F(g(x)) is f(g(x))g'(x), it makes no sense to change x to f(u). Also if one had the function (x^3)/(thirdroot(x^3+4)), my book says:

The substitution u=thirdroot(x^2+4) leads to the following equivalent equations:

u^3=x^2+4, x^2=u^3-4

Taking the differential of each side of the last equation we obtain

2xdx=3u^2du

Is it legitimate to do that? All I can make of this is that they implicitly differentiated x^2 with respect to u and then multiplied both sides by du, but obviously you cant treat dx/du as a fraction? Or can you?

The way I learned it is this:

First, let's define a function $f(x)$ and it's inverse $g(x)$. So, we know that:

$f(x)=g^{-1}(x)$

and, therefore,

$g(f(x))=x$

so, using the chain rule:

${\frac {d}{dx}}f(g(x))=f'(g(x))g'(x)$

$g'(x)={\frac {1}{f'(g(x))}}$

Now, you know that:

${\frac {d}{dx}}arctan(x)={\frac {1}{sec^{2}arctan(x)}}$

And, using this variant of the pythagorean theorem:

$sec^{2}x=1+tan^{2}x$

You then get:

${\frac {d}{dx}}arctan(x)={\frac {1}{1+(tan(arctan(x))^{2}}}$

and voila!

${\frac {d}{dx}}arctan(x)={\frac {1}{1+x^{2}}}$

Hope that helps.

Sameer Kale 01:37, 30 April 2007 (UTC)

Hello- Problem sets and Implicit Differentiation.

Hello. I was thinking about adding some problem sets with worked out solutions to the differential calculus sections. Also, no one has added an i mplicit differentiation section or worked problems/problem sets. I was thinking about doing that in the section after the chain rule. Good or bad idea?

Sounds like a good place for it since implicit differentiation is basically just the chain rule applied. (PS it's a good idea to 'sign' entries on talk pages with three tildes, like this: ~~~ It will show up on the page as your username, adding a forth tilde will add the date and time.) Grimm

Move to new naming policy

I believe it's time to consider converting this entire book to the new Wikibooks:Naming policy (using slashes instead of colons — for example, Calculus:Differentiation:Exercises would become Calculus/Differentiation/Exercises). There appear to be 80 pages starting with "Calculus:" that would need renaming (i.e., moving). The changing of individual links can be accomplished with a bot (it's around here somewhere) or worked on "by hand" at a leisurely pace, since redirects will exist from the old names. Any strong objections? - dcljr 19:57, 18 May 2006 (UTC)

Looks like User:Jguk has made the required changes. Thanks. (Although, as I suggested above, I would have left redirects in place so that links from external sites to the old page names would still work.) - dcljr 18:09, 19 June 2006 (UTC)

sources of GFDL'd or PD problems

Several people have commented on the need for problem sets. One source of problems, available under GFDL, is m own book. The latex source code is available through its web page, and I would imagine it would be pretty easy to convert problems for use here, since mediawiki uses latex for math. Solutions are given in the back of the book for all the problems in the early chapters. Another source of problems is Thompson's Calculus Made Easy, which is public domain (at least the original editions are).--Bcrowell 17:47, 4 June 2006 (UTC)

I agree that problem sets would be great, seeing as practice is the most important part of any calculus course. The answers should not be presented immediately, either (i.e. problem-solution-problem-solution), but in separate chunks so a motivated individual could go through and solve them en masse and actually learn something by it (i.e. problem-problem-problem, solution-solution-solution).--Fyedernoggersnodden 19:11, 4 November 2007 (UTC)

I started Calculus/Infinite series/Exercises, once upon a time. My format: a section of several problems, followed by a section of hints, then a section with answers only, and finally a section of complete solutions. - dcljr 02:22, 18 November 2007 (UTC)

L'Hospitals rule?

Does this book have a section on L'Hospitals rule? I looked in the "applications of derivatives" page, but it wasnt there (that i could find). --Whiteknight(talk) (projects) 15:19, 27 June 2006 (UTC)

I thought I created for L'Hôpital's when I first joined the project. The book has changed a lot since then, though. I am going to go through all the pages next week. I know a couple pages are orphans, I think others are effectively orphans, and I'm pretty sure there is some redundant material. Cheers, Iamunknown 05:27, 10 December 2006 (UTC)

Infobox has been created

I am not familiar with this book's history and would like for a usual editor to enter the infobox information. Help can be found at this link. --Herraotic 21:34, 26 December 2006 (UTC)

Archive

I am going to archive this page if there are no objections--Cronholm¹⁴⁴ 08:18, 18 June 2007 (UTC)

Less than optimal state

I have been working on this book for about 5 hours now and there seems to be no end to the work needed. Clean up of existing sections is desperately needed as well as expansion on anything marked 25% . This is not a textbook as it stands now, but it can be, if a concerted effort is made. cheers --Cronholm¹⁴⁴ 11:39, 19 June 2007 (UTC)

Pictures are desperately needed, cull them from wikipedia--Cronholm¹⁴⁴ 11:41, 19 June 2007 (UTC)

Proposed style

See my user subpage User:Cronholm144/Calculus--Cronholm¹⁴⁴ 01:39, 20 June 2007 (UTC)

Explanations

I would like to see a little more explanations and discussion to go along with the simple theorums. In general there are three ways to understand any mathematical method. by its proof, its graphical geometry, or its algorithm. There needs to be explanations of all three ways. Preferably these explanations should be written by someone who remembers what it is like to not know these things. Someone who learned this and has been using it for a few years but not long enough to think it is self explanatory.

Worked on Adding a Limits Section

Dear Calculus co-authors: I have expanded the book to include limits section because the limits page was getting quite long. If another approach to the book's organization is better, let me know Gwilm (talk) 03:29, 20 February 2008 (UTC)

Newton vs. Leibniz

There's no mention in the introduction of the two notations. Should this be added? In most of the differnetiation articles, Leibniz notation is used but not in the article devoted to Implicit differentiation. Should this be fixed? Battlebison (talk) 01:38, 30 March 2008 (UTC)

Common notations are mentioned in Calculus/Differentiation#The Slope at a Point (edit: and have a heading at Calculus/Differentiation#Understanding the Derivative Notation). I think pages should use one notation or state their reasons for using another. --Mrwojo (talk) 00:05, 29 December 2008 (UTC)