Talk:Calculus/Archive 1

question about vectors
Shouldn't vector stuff be in a Higher Algebra section? If anyone doesn't mind, I'll move it in there and add to it later... Dysprosia 08:34 5 Aug 2003 (UTC)

Sure.... I encourage people to modify the Calculus textbook extensively, as I will be rather busy until around May when summer vacation starts and I have some free time :).  I have some stuff intended for the limits page that I haven't gotten around to proof-reading and submitting.  -- IntMan

Calculus Book
Has anyone thought of doing an anti-Calculus book (one using non-standard analysis and infinitesimals)? I think the approach is more natural and can be made rigorous.

If want to do a non-standard analysis, I would suggest doing P-Adic analysis.

You can do non-standard analysis along side any regular calculus book. Really the only difference would be on the formal section on the definition of a limit. It would be easy to write a "drop in" replacement of that section. -- julius

Environments
This books needs a uniform method for presenting
 * 1) theorems
 * 2) definitions
 * 3) examples
 * 4) solutions
 * 5) others?

For definitions and theorems we really need per-page css. Maybe this will appear in a future version of wikipedia.

The following are some alternatives none of which seem great

Just use section headings?
One way is just to use section headings. Advantage: you can edit a smaller portion of the page. Disadvantage: the contents page gets a little cluttered.

Blockquote
I now think this is a bad idea as the wiki formatting does not behave well with blockquote usage Juliusross 15:34, 22 October 2005 (UTC)

Using the nonwiki blockquote presents theorems and definitions well:



Theorem: Fundamental Theorem of Algebra
Every non constant polynomial defined over the complex numbers has at least one root.


 * Disadvantage:
 * Line breaks, math and wiki markup can become a total mess.
 * bad breaking when printing (we really want the whole box to remain on a single page)
 * Editing the "theorem" above does not show the 'blocktext'' markup. So the "preview" does not give the correct result.

Templates
One option is to use templates. For instance gives . This seems to be a bad idea as they are not numbered and cannot be refered or linked to. Also it is not clear how large the parameter can be.

Presenting math
A suggestion: Displayed equations should done as follows to get the alignment correct (hopefully this will not be necessary in some future version of wiki software).


 * 1) Inline equations should be done using $$blah$$ (rationalle: it looks better and more consistent, and maybe if blahtex or some similar becomes used it will look better).
 * 2) Displayed equations
 * $$ blah $$


 * 1) Multilines to be presented at

{| line 1M \\


 * line 1M \\


 * line 1M \\

}

Misc

 * 1) Do we say limits "diverge" or "equal infinity".  Probably the second
 * 2) Formulae which end sentences should end with a period.
 * 3) Prefer sin2 x rather than (sin x)2  (I know the latter is more precise, but the former really is standard).
 * 4) No math markup should appear in headings (they look terrible in the contents page)


 * Wouldn't it be more appropriate to say limits "approach infinity" since infinity is more of a concept than an idea? Both terms should be used interchangeably as it increases the fluency of the student.

ChaoticLlama 17:57, 20 March 2007 (UTC)

Graphs
1. For graphs. There is a site, wikisophia, that generates gnuplots graphs; http://wikisophia.org/wiki/Wikitex_Plot No reason on earth not to use it, especially as the code may be integrated into wikimedia at some point. This means code to generate the plot should be a comment next to the actual graph, especially for easy re-writes and changes.

Calculus of variations
I'd like to have something on the calculus of variations somewhere. Do you think it would be appropiate for this book, or would better belong somewhere else?


 * No, go ahead. Sounds great :) Dysprosia 04:44, 5 Jun 2004 (UTC)


 * I disagree. Calculus of variations is not usually considered in the same vein as regular calculus (e.g. to do it properly requires some functional analysis).  juliusross

Solved Examples and Problem Sets
I was thinking about adding a few solved examples and problem sets. If I suddenly forgot calculus, I don't think I could simply read a few of the pages within and be ready to differentiate or integrate. I believe adding solved examples and practice problems would benefit anyone attempting to study calculus. I realize that some of the explanations given will not be adequate for solving an example problem, and I would not have any problem updating the explanations to do just that.

Spammy


 * Please do. I've added dead links on the section pages to pages of exercises on each section page. I used the naming convention 'Calculus:[section name]:Exercises' for consitency it would seem natural to use 'Calculus:[section name]:Solutions' for the corresponding pages of solutions.Grimm 01:07, 1 May 2005 (UTC)

There do exist some large collection of exercises (e.g. webworks). I do not know what license they are under though. It would be far easier to integrate these then to write new ones. Juliusross

Someone should put some excersises in Further integration techniques

Table of Contents vs. Outline
Hey folks, great to see this wikibook. It looks like it will be a great help once I start my calc classes this summer. On the front page, it is very easy to skip over the line that tells the user to go to the outline page. I missed that line the first time I looked at the book, and only saw it when I came back a couple of hours later. Originally I was a bit disappointed - thinking the book had almost no content yet (b/c TOC links are dead). Perhaps the TOC could be replaced by the outline? at least until a new updated TOC is developed... David March 30, 2005


 * I would agree. The outline, as it stands, makes a better main page than the main page does. Grimm


 * ...and unless someone comes along and disagrees I'm going to start moving things. Grimm 01:19, 30 Apr 2005 (UTC)


 * what is the difference between this page and the "development outline" page?

New Main Page
I've begun reworking the main page from the outline. I've changed Template:Calculus:TOC to a navigation template with links to the main pages of the major sections. Thus far the section pages only have links to articles but they should have introductions to / brief discussions of the subject matter eventually.

I've added dead links to section pages of exercises on each section page. I used the naming convention 'Calculus:[section name]:Exercises' for consitency it would seem natural to use 'Calculus:[section name]:Solutions' for the corresponding pages of solutions.Grimm 01:03, 1 May 2005 (UTC)


 * Pages orphaned by the reorginization (struck out where useful information has already been removed):
 * Chapter 1 - Limits and their Properties
 * Chapter 2 - Differentiation
 * Chapter 4 - Integration
 * Chapter 6 - Exponential and Transcendental Functions
 * Chapter 7 - Further Methods of Integration
 * Chapter 8 - Infinite Series
 * Chapter 9 - Conics, and Parametric and Polar Equations

Just a note of thanks
Thanks to all those who worked on creating this Wikibook. I'm finding it quite useful for refreshing my memory of calculus. It's great to have this available, and editable, and of such good presentation and apparent quality. Thanks! w:en:User:JesseW 07:37, 11 Jun 2005 (UTC)

A-level Mathematics
What are the restrictions on this section? Am I allowed to copy parts out of here and change it slighty to fit in with the A-level Mathematics module that I'm contributing to? -- Krackpipe
 * Of course, all text on Wikibooks as well as other Wiki's sponsored by the Wikimedia foundation are under the GNU Documentation License which allows you to modify and copy if you will also allow your text to have the same usability. --Herraotic 19:00, 5 December 2006 (UTC)

Downloadable books
Perhaps we should get this in a downloadable form and attach extra chapters for optional homework. Having it downloadable into pdf or pd form would increase the usefulness alot

It is a good idea but is not yet possible on wikibooks.

Just saying hello
hello everyone I thought I'd say hi to everyone. I'm going to add some stuff that seems to be missing like implicit Differentiation and some of the applications of integration. --Stranger104 14:51, 22 August 2005 (UTC)

any prequist?
i dunno any calculus but i really want to learn it because all so many math stuff use it and gives amazing formulas i can understand, except i dunno how it is proved. so is this a introduction to beginners or intermiate stage?

thanks -protecter


 * It will probably work as an introduction for people who have not seen any calculus before. Prerequisite would  be  algebra and maybe some trigonometry.


 * There are many prerequisites to Calculus that you must have a firm grasp of before you may continue. Algebra must be perfect, you must also be comfortable with trig, logs, exponentials, systems of linear equation, polynomial division, functions/funcational notation and their analysis and time and patience enough to being actually learning math.

Little More explanation?
I find it impossible to self teach yourself calculus from this book since whenever it comes up with an equation it doesn't explain how to come up with the equation in the first place. (for example: the first paragraph of the second precalculus chapter, 'x is an element of' notation also needs some more explanation. I think as i go on i'll just find more stuff that needs more explanation to be understandable.) --V2os 21:48, 7 September 2005 (UTC)