Introducing myself to calculus

[DanM]

NO, NO, JUST NO!

Yes, it has to be in caps. If you wanna learn Calculus and Physics, stay away from Wiki and find good books.

In my opinion, the biggest issue with Wiki (aside from accuracy) is that it appears to be written for an audience already familiar with the information which it presents.

Anyway, are there specific book titles that I should look for? I'm not quite looking for a textbook, but one that is meant to be read through and includes problems at the end of each chapter.

 

[Quick_Nick]

In my opinion, the biggest issue with Wiki (aside from accuracy) is that it appears to be written for an audience already familiar with the information which it presents.

Anyway, are there specific book titles that I should look for? I'm not quite looking for a textbook, but one that is meant to be read through and includes problems at the end of each chapter.

Consult your school's calculus teacher if possible? Maybe borrow a textbook.

You're right about wikipedia. With most of the sources I found, I didn't fully GET what I was reading, but read anyways. The basics of differentiation and integration are really simple operations however. The class then filled in the gaps for me, so I could then make connections about what I had previously researched.

 

[Jarvitä]

In my opinion, the biggest issue with Wiki (aside from accuracy) is that it appears to be written for an audience already familiar with the information which it presents.

The biggest issue is that there's no way of knowing whether or not the page you're reading has just been purposefully filled with misinformation, short of hunting down every reference (if everything is referenced). You'd be surprised how long it takes math pages to get anti-vandalised after subtle changes, compared to the article on Lady GaGa.

 

[DanM]

The biggest issue is that there's no way of knowing whether or not the page you're reading has just been purposefully filled with misinformation, short of hunting down every reference (if everything is referenced). You'd be surprised how long it takes math pages to get anti-vandalised after subtle changes, compared to the article on Lady GaGa.

Exactly. It is by no means a good idea for one to base their education off of Wikipedia. What the website is best for would be gaining general information on a topic and pictures.

 

[toddhisattva]

Motivation

Calculus for computers? :huh:

Yes, oh Great Gauss yes! It has to do with the motivation for making these computer thingies in the first place. Calculus is (these days) taught through limits, which is how to add up an infinite number of infinitely tiny things to get a useful number. Approximating that gets very tiring for a human. Liebniz, the co-inventor of calculus, spent some time at least dreaming of a machine to relieve mathematicians of this laborious figuring. As recently as WW 2, a "computer" was someone like Françoise Ulam, crunching numbers for her husband at Los Alamos.

Calculus will get you the mathematical constant "e." Your floating-point units are built around this constant and pi. Those are the only two far-out-n-funky numbers in all of computer mathematics. Trig is done by raising e to imaginary powers. Your school certainly does not want to graduate someone who doesn't know this, and it sounds like they'd rather not teach you so they make it a requirement (the ways of schools are a mystery to me and I tend to giggle during the chanting^H lectures anyway).

Places like iTunes University and MIT's Open CourseWare are great. Wikipedia is of course good for a quick consult, examples, proofs. Wolfram Mathworld is excellent and is perhaps "too good" because I get distracted by the fascinating clicky-links!

You'll learn to get to e by taking a limit of the compound interest equation (I learned that at a young age from a side-note in a 1970s T.I. programmable calculator manual, forever cementing in my mind the usefulness of computers to explore mathematics). You'll learn about Madhava-Taylor series to get there too.

When you "get it," you'll be having fun.

Hail probe!

On a slightly different subject, I agree that "pre-Calculus" is useless. Dive in! Drink deep! There is one thing more useless, and that is "pre-Algebra." Do these schools teach swimming with a whole year of wading?

 

[Scav]

:lol:

Nah, the biggest problem I've had with algebra so far . . . is that I hadn't studied it since high school, and their idea of a class duration is five weeks.

It's going to be very interesting studying, disseminating and dissecting the properties of 'e.'

 

[DanM]

Are there any ways I can utilize Microsoft Math in learning Calculus?

 

[RisingFury]

I didn't know what calculus meant until about 1.5 years ago, and now it's pretty much all I do in maths, and it shows up in physics too.

If "it shows up in Physics too", it means you're still very young :lol:

I honestly can't imagine Physics without calculus.

 

[RGClark]

In my opinion, the biggest issue with Wiki (aside from accuracy) is that it appears to be written for an audience already familiar with the information which it presents.
Anyway, are there specific book titles that I should look for? I'm not quite looking for a textbook, but one that is meant to be read through and includes problems at the end of each chapter.

You can read other books if you want to but I really think you should read the assigned textbook beforehand. Also download the professors syllabus to get an idea what sections you will cover. Almost nobody covers all the sections in a calculus book because there is so much material.
Most calculus books have a preliminaries section where the basics of the algebra you'll need is reviewed. However, not all professors choose to review those sections. That's another reason to look over the syllabus your professor will use. If the professor does not have a course web site where you can download the syllabus, send him an email and ask for the syllabus.
Look over the preliminaries sections in the textbook and be sure you are strong on the algebra you'll need to know. If you are shaky on some topics then read through that section and try to do some of the problems. You can also use your previous algebra textbook and notes for a more familiar reference point on those topics you need to review.
Once you feel you are strong on the algebra in the preliminaries sections, try reading the beginning calculus sections and see if you can do the exercises. If you get stuck on some points, you can ask on this forum.

Bob Clark

 

[DanM]

Wolfram MathWorld is probably the best math resource I have found on the internet. Which articles should I read to provide myself with a better understand of Calculus?

 

[Quick_Nick]

I always found MathWorld to be confusing. And since it doesn't follow any order, you need a book or class to direct you to the next section. The information is fairly short and there aren't many examples. (though you can make up some for Wolfram Alpha and see the work)

 

[Jarvitä]

Wolfram MathWorld is probably the best math resource I have found on the internet. Which articles should I read to provide myself with a better understand of Calculus?

That honestly doesn't strike me as a good idea. MathWorld is more of a reference than a learning guide. It's great if you're looking for very specific information about a subject you're already familiar with, but I honestly don't think I could have learned much from it from scratch.

To start with, how understandable are these articles to you?

http://mathworld.wolfram.com/Limit.html
http://mathworld.wolfram.com/Derivative.html
http://mathworld.wolfram.com/Integral.html

 

[Urwumpe]

I liked Wikipedia for getting a quick overview in the concepts, before diving into the library for getting the stone-cold facts. I found many good solutions in the math lecture homeworks by seeing more than just the exact formula.

 

[Jarvitä]

I liked Wikipedia for getting a quick overview in the concepts, before diving into the library for getting the stone-cold facts. I found many good solutions in the math lecture homeworks by seeing more than just the exact formula.

Did you always check the edit history to make sure the article you were looking at wasn't a victim of this?

 

[Urwumpe]

Did you always check the edit history to make sure the article you were looking at wasn't a victim of this?

Usually yes, but after trying to make sense of what is written there. If I can't understand it, it is possibly wrong or at least, the wrong formula for me.

 

[DanM]

That honestly doesn't strike me as a good idea. MathWorld is more of a reference than a learning guide. It's great if you're looking for very specific information about a subject you're already familiar with, but I honestly don't think I could have learned much from it from scratch.

To start with, how understandable are these articles to you?

http://mathworld.wolfram.com/Limit.html
http://mathworld.wolfram.com/Derivative.html
http://mathworld.wolfram.com/Integral.html

Thank you for pointing out that flaw in my plan. Those articles made virtually no sense to me. However, I decided to use websites oriented towards people learning these concepts for the first time and I figured out limits in almost no time at all.