Talk:Calculus

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todo-list of Calculus

You know about this? http://mecmath.net It looks in terms of licensing like it can be incorporated into the wikibook, and maybe the author would like to participate. —The preceding unsigned comment was added by 207.241.238.217 (talk • contribs) 04:46, 2 July 2008 (UTC)

Hello, I'm fairly new to Wikibooks but interested in helping on this chapter. Would anyone be willing to give me an overview of the goals and organization, as well as where the most help is needed

Hearing no objections, I'm planning on doing some reorganization of the Integration Techniques modules. I would love to get some input from the community, let me know. W3asal (talk) 05:32, 20 September 2008 (UTC)Reply

If anyone else is currently working on this book, let me know. I'm planning on doing major rewrites of several sections (starting in the Applications of Integration), and I'd love to coordinate with others. Leave me a message below or on my talk page. Thanks, W3asal (talk) 01:27, 28 January 2009 (UTC)Reply

Is there a standard style for stating theorems in this book? —The preceding unsigned comment was added by 199.170.84.172 (talk • contribs) 09:39, 7 October 2008 (UTC)

This book seems to lack a contributor's guide or local manual of style. --Swift (talk) 06:36, 13 February 2009 (UTC)Reply

I've created {{Calculus/Def}} for this sort of thing.

The old Calculus/Outline resembled a contributor's guide, so I've expanded it at Calculus/Contributing. --Mrwojo (talk) 16:28, 8 September 2009 (UTC)Reply

I would agree with this merger. Unless there are objections, I will be happy to start this process. --Shiftout (talk) 23:11, 29 October 2008 (UTC)Reply

The merger sounds like a good idea to me.Thenub314 (talk) 19:13, 20 January 2009 (UTC)Reply

I've moved the merge notice to the appropriate sub-page. Go ahead and be bold. --Swift (talk) 06:12, 13 February 2009 (UTC)Reply

I've just expanded the TOC on the main page. While the collapsed version may be more contributor friendly, those who are new to calculus and unfamiliar with the book structure benefit from a more detailed view. To further help them catch their bearings (and pretty this up a bit) I've added some relevant images to the first few sections. --Swift (talk) 06:11, 13 February 2009 (UTC)Reply

Is there a policy on the number of examples/worked problems within the text? I think more examples would be of great value. Secondly, I'm curious as to the intent of the book. Certainly, someone looking for a survey of calc text would not be served well by this book but the content they want/need is within. Any suggested reading ideas? Tiled (talk) 17:47, 17 November 2009 (UTC)Reply

I think lots of examples is a good thing. However, the exercises have solutions so it's not that important. I mean, you should have enough examples to show how to do the standard calculations/problems. Beyond that, people can just look at solutions to exercises if they need more help. So, an extra example won't hurt anything either probably, but once there are a good amount of examples, you could just add to exercises maybe. This is just what seems good to me at the time but I'm not saying it is definitely the best way.

I'm not sure what your second question is supposed to mean. This is just a calculus book like any other calculus text, at least that's what I assume. What do you mean someone looking for a survey of calc text would not be served well by this? If you just want a survey of calculus, skip some sections. All the basics are here, as well as nonbasics. Of course, the book could use a lot of work but it's certainly got a lot of good stuff in it already. NumberTheorist (talk) 20:42, 17 February 2010 (UTC)Reply

The exercises in this book need lots of work. I will work on them a little but they could use a lot of work. For example, problem 8 in Differentiation is currently to find the derivative of ${\displaystyle x^{3}*2{\sqrt {y}}}$ and the solution is given as ${\displaystyle {\frac {x^{3}}{\sqrt {y}}}+6{\sqrt {y}}x^{2}}$. Hopefully if you're helping on this book, you understand that this makes no sense, sort of a hybrid of a derivative with respect to x in some parts and with y in other parts. And, the exercises have all sorts of formats. This looks bad. Also, some come in the middle of the section and some come in their own section at the end. This is actually fine if we want to do it that way but it's probably best to just put them all at the end in one section (or to have all exercises pertaining to a certain section at the end of that section). Any way, point is all aspects of exercises need work and I will do only a little work so need lots of help. NumberTheorist (talk) 02:39, 18 February 2010 (UTC)Reply

Okay, for starters, what are opinions on where exercises should go? My vote is they should be at the end of each section because there are too many topics per chapter to have them all there. For example, currently we have a chapter Differentiation with sections

Differentiation - An introduction

More differentiation rules - More rules for differentiation

Higher Order derivatives - An introduction to second power derivatives

Implicit Differentiation

Exercises

My thought is we do away with the section Exercises altogether and we put exercises at the end of each of the 4 other sections. This is how your typical calculus book does thing. NumberTheorist (talk) 02:46, 18 February 2010 (UTC)Reply

I suggest that each module end on an exercise section with problems that specifically practice the concepts just covered. We could also collect the exercises into a special set of modules, but little is gained and it would make keeping the content up to date harder. --Swift (talk) 10:10, 18 February 2010 (UTC)Reply

Hmm, well, I don't know the terminology here :) What's a module? If you look above, you'll see my terminology. Differentiation is a chapter and then there are 5 sections under it, Differentiation through Exercises. I am saying, and perhaps you are too, that exercises should go at the end of each section. This is what basically any calculus book, and almost any math textbook, would do. It would be way too confusing to cover all of differentiation and then go to the exercises. You need to cover a little bit and then have focused exercises on those concepts. Then, cover a bit more and do some exercises, and on and on. All of the Differentiation chapter covers a ton of material, equal to at least 9 sections in the calculus book I am teaching from right now. NumberTheorist (talk) 16:00, 18 February 2010 (UTC)Reply

Also, I realized that most calc books have a section at the end of each chapter with additional exercises, so it's not wrong to put them at the end of a chapter but there need to be exercises at the end of each section, if you ask me. NumberTheorist (talk) 16:02, 18 February 2010 (UTC)Reply

And, sorry, but I looked up what a module is and it seems that we agree if I understand it correctly. NumberTheorist (talk) 16:15, 18 February 2010 (UTC)Reply

Yes, we seem to see this the same way. --Swift (talk) 22:47, 18 February 2010 (UTC)Reply

I am assuming that the question-answer template is OK for all exercises? I love it. I will be sandboxing some multivariate exercises, and will try to include them here in the next few weeks.

I dumped a bunch of multivar calc exercises in the corresponding sub-section (it used to be empty). Some of them in the beginning may be more properly located in single-var calc, and the reason they are there is because I used them as a part of review in a multivar calc course. Of course, now we can move them, as long as they work with the text already written. Another area where more work is almost certainly needed is the consistency of the notation: I didn't look very carefully, so some of the notation I used (which is the same as that used by Stewart and Sullivan, and is pretty standard) may be in conflict with the text already written. I believe, though, that many exercises may be used as they are. Melikamp (discuss • contribs) 18:04, 8 January 2014 (UTC)Reply

1. Should we introduce some sort of numbering system, such as Precalculus is labeled Chapter 1 and Limits is Chapter 2 (some books might make Precalculus Chapter 0 and Limits Chapter 1)? And, then below that, sections being labeled. And, how should this be done? Should it be Chapter 1, then Section 1, or we could do an outline form, I and then 1 and then a and so forth? Or other?

I'm against the idea of numbering systems. They serve little purpose and make restructuring content a pain. --Swift (talk) 23:11, 18 February 2010 (UTC)Reply

2. Does it make sense to put solutions to all exercises? If so, where should these go? Should there be a link to the solutions? Should we just Hide the solutions so you click on "Show" and they pop up?

I think solutions to all examples are a good idea. Something along the lines of {{DropBox}} might be useful. --Swift (talk) 23:11, 18 February 2010 (UTC)Reply

3. What is the standard format for an exercise? I see some putting the \, in to make the math bigger and then I see some without it. And, if you have a question, such as "What is the area of blah blah blah ${\displaystyle f(x)=6x}$?", what do you do with that if your general rule is to make all the math type bigger?

That's a good start I guess. NumberTheorist (talk) 16:30, 18 February 2010 (UTC)Reply

There doesn't seem to be a standard format. Just be bold. The format can always be changed later. --Swift (talk) 23:11, 18 February 2010 (UTC)Reply

Without going into extreme detail, this section has the amount of material in about 5-8 sections in your normal calculus book (I've looked through 2 different ones and I think it's 5 sections for one and 7 or 8 for the other). So, it seems to me this section should be split up some. It could be done in many ways probably. Any thoughts? NumberTheorist (talk) 16:51, 18 February 2010 (UTC)Reply

I think this content would best be split in four along the level-two headings: One for the chain rule, another for the product (and quotient) rule, a third for implicit differentiation and a fourth for derivatives of common functions. --Swift (talk) 23:19, 18 February 2010 (UTC)Reply

Hmm, I was thinking more like separate pages (or modules might be the right word). The reason I thought that was because of exercises. Right now, it seems like too much material to go through before having exercises. If it were split at least in 2 or 3 or 4 modules (for example, your suggestion), then there would be less material before the exercises show up and it seems like this would be easier to learn from. What do you think? NumberTheorist (talk) 23:49, 18 February 2010 (UTC)Reply

Yes, that was what I was talking about: To split the content (up into separate modules/pages). --Swift (talk) 00:51, 20 February 2010 (UTC)Reply

Alright, hehe, I guess I need to get down this new vocab. I think your four headings are good but with the added point that product and quotient rule should come first. I noticed that in the discussion on some page, maybe this one, it was already mentioned by one person and agreed by another that those are easier and should come first. They came first in the 2 calc books I looked at. NumberTheorist (talk) 03:01, 20 February 2010 (UTC)Reply

Upon looking at it again, I have a couple thoughts. First off Implicit Differentiation is already a section so the implicit differentiation part of this section should just be merged with the implicit differentiation one that is already there. Beyond that, it might be nice to do the derivatives of trig functions before the chain rule, as you only need the quotient rule to do them, so that you can have a little more variety than just a polynomial to a power. And, technically you use implicit differentiation to prove the derivative of logs and also of inverse trig functions. So, I propose we put inverse trig functions in the implicit differentiation section and then after that put exponential and logarithm functions as another section. I will create these sections right now. NumberTheorist (talk) 03:14, 20 February 2010 (UTC)Reply

I put in the top nav bars for each of the new pages and labeled them to not included "More Differentiation Rules". As far as that section, I moved all the exercises to the Exercises section temporarily. I did notice all the new sections are showing up under Subject:Calculus but maybe they will go away now that I deleted BookCat from each one. I don't know what causes that. NumberTheorist (talk) 22:34, 20 February 2010 (UTC)Reply

Contents page is too long. I propose we stick to just major sections on the contents page, and their subsections. Links to subsections introduce the subsection and show the contents of its pages. Links to major sections show table of contents for the whole section. I believe this was what was originally planned (from the contribution page) but seems to have been drifted away from. Italienmoose (talk) 19:31, 5 June 2010 (UTC)Reply

Dude, I'm in totally agreement with you on the length. Personally, I don't think that this wikibook should be one giant treatise, like the popular Stewart Calculus book. That book is over 1,100 pages. That's too long, too much content. It takes about three semesters to go through the whole thing. That's the real reason why this contents page is too long. If this book, with its current ambitions, was seen to total fruition, it would be way long. If anyone ever wanted to make a physical version of it, you could use it for crushing. Anybody else think it would be smart to split this book up? Tiled (talk) 22:20, 26 August 2010 (UTC)Reply

Uhh, it covers the material that would be 3 semesters at most colleges. And, most colleges would use 1 textbook for such a course. I own 3 different calculus books (one begin Stewart's) and teach from another and they're all essentially the same, as far as the main topics covered goes. I say it's smart to leave this wiki book as is. Perhaps you could do, as most textbooks do, and make several editions of the book. There could be a single variable version, a multivariable version, an early transcendentals version, whatever. But, this one book should stay together as it is a standard list of topics for one textbook. I will admit it may have a few sections here and there that wouldn't be in a standard calculus book but that's the beauty of an online book. We don't have to exclude topics to save money in printing. NumberTheorist (discuss • contribs) 19:20, 26 April 2011 (UTC)Reply

This book (at least in the printable version) ends with a copy of the GFDL. I think it should be removed since now wikibooks is under CC-BY-SA. Can I do it, or am I wrong? Fale (talk) 16:45, 9 June 2010 (UTC)Reply

I don't have a problem with it. The whole point of moving to CC-BY-SA was to avoid having to include the full text of the GFDL with every instance of the content. – Adrignola ^{talk contribs} 16:58, 9 June 2010 (UTC)Reply

Go ahead and remove it, this was indeed one of the benefits of relicensing. Thenub314 (talk) 17:40, 9 June 2010 (UTC)Reply

The section titled "Infinite Limits" should be titled "Limits at Infinity". The definition is for "limits at infinity" and we talk about limits at infinity for rational functions. The discussion is almost exclusive about finite limits at infinity. Only the last example is an infinite limit. Chrislmorin (discuss • contribs) 16:20, 27 January 2013 (UTC)Reply

I agree. I plan to make the change in the near future unless anyone has any objections. Greenbreen (discuss • contribs) 10:13, 21 May 2016 (UTC)Reply

I think that the sequences and series section is in dire need of some TLC. I think it should be broken up better, like the other sections, and I think even simple topics like geometric and arithmetic sequences should get their own page. Right now, all the tests for convergence are on one page and I think it's just kind of ugly and unorganized like that. Lazauya (discuss • contribs) 15:54, 19 August 2017 (UTC)Reply

I personally think @Mathmensch:'s content is quite pure and abstract to be considered as core (eg: Calculus/The_chain_rule_and_Clairaut's_theorem). I doubt someone looking for help with multivariate calculus (eg a college student) will be able to grasp what they've written, as to me it requires a significant background in real (and even functional) analysis. My proposal is to hence move them to the extension section. Leaderboard (discuss • contribs) 18:47, 16 April 2022 (UTC)Reply