Learn Calculus Independently: Advice for Keith

[revelator]

Just a question. I've never really had any problems learning and grasping math. Unfortunately I chose not to continue my formal education past the high school level.

I find myself these days, wanting more and more to learn the advanced mathematics, so I can get a better grasp on physics.

So my question is, do you suppose it is possible for me to properly learn calculus independently (as I don't know any individuals whom I can approach with any technical questions on the matter)? If so, could someone recommend texts to me which I could purchase?

Thanks very much.

Regards,
Keith

 

[phoenixthoth]

yes you can do it on your own.

you can call up your local college's bookstore and ask them for what text they're using.

the standard texts are by stewart and the reform calculus is by hughes-hallet, et al.

if you want to really learn it well and risk getting overwhelmed, pick up spivaks's mighty calculus text which i would use for an honors calculus class.

 

[revelator]

I suppose then that the most prudent course of action would be to first thoroughly learn the standard texts. And then, provided I still want to learn more, learn the text that would be used for an honours class?

 

[phoenixthoth]

i would recommend reading stewart in conjunction with hughes-hallett (sp?). read up to and including "integration." in the 2nd edition of stewart, chapters 1-8 would take you into the beginning of a second semester course in calculus.

even if you want to do something not trivial but not string theory, like the heat equation, you need calculus of multiple variables as well as "partial differential equations" but chapters 1-8 would be the basis for any of that.

once your there, start looking into books with titles "mathematical physics" or "math for physics" which will probably have calculus as a prerequiste as well as other things.

if you could read chapters 1-8 in stewart and hughes-hallet, then read the equivalent in spivak's "calculus" (which may, sadly, be out of print), not to be confused with his "calculus on manifolds", you will gain even more insight into the reason why things work the way they do. perhaps his book should be called "calculus revealed." however, stewart doesn't do a bad job at all and neither does hughes-hallet.

if those are "too difficult" then get hughes-hallet's, or anyone's, book on "applied calculus" which is for those not going into science. it may be a good precursor to the medium level calculus. the medium level calculus like stewart, as opposed to the hard calculus like spivak, is what science majors have to take. especially if you're doing it on your own, there's no shame in doing this precursor first.

i may be way off base but hughes-hallet seems to be more concerned with the pedogagic level of the book than stewart or spivak perhaps to some people's minds at the cost of mathematical rigor.

 

[revelator]

Just to be certain, is there anything I should know as a pre-requisite to calculus? I don't want to jump into calculus lacking the necessary background.

 

[phoenixthoth]

you have to be fully comfortable with algebra and functions and know basic trig.

for example, if f(x)=1/x, then you should be able to calculate and simplify (f(x+h)-f(x))/h.

(that one should be, for example, -1/(x(x+h)).)

 

[revelator]

Okay then. Just to verify the titles of these books (wouldn't want to get the wrong ones, textbooks are expensive).

I'm going to want to get and learn:

Calculus by James Stewart
Calculus by Deborah Hughes-Hallett

If I find difficulty with them, then I should read

Applied Physics by Deborah Hughes-Hallett

which should serve as a decent buildup to the first 2.

And once I've mastered it, I should move on to

Calculus by Michael Spivak

 

[matt grime]

Do not buy any textbook used for freshman calc, or similar. they are overpriced and aimed at a captive audience. there are plenty of free study aids on the internet. the calculus in those books is a poorman's version of calc as the mathematician would understand it. if you want theory aim higher, if you want application go and get a physics book. if you buy any of the undergrad (US) books you will be wasting a lot of money on something that will not last you very long or help you later.

 

[meister]

I would hardly say that the Calculus learned by pretty much everyone in their undergraduate courses is a waste of time.

And clearly this guy isn't a "mathematician," so I would argue that Stewart would be just fine. Especially since you can buy it on ebay for cheap, especially an older version.

 

[matt grime]

Originally posted by meister
I would hardly say that the Calculus learned by pretty much everyone in their undergraduate courses is a waste of time.

And clearly this guy isn't a "mathematician," so I would argue that Stewart would be just fine. Especially since you can buy it on ebay for cheap, especially an older version.

I didn't say the calculus wasn't worth it, but that the books you may learn it from *may* be. For example, there is at least one book, whose author's I can't remember (but it is widely used) that teaches 3 'different' chain rules. Why? Just overly confusing and pointless I reckon.

If you can get a cheap one, fine, but forking out money for undergrad level texts seems like a pointless expense, especially considering the standards of mathematics I've seen inside some of them. Try getting some physics or engineering textbook. And use the rule of thumb that the more the title emphasizes how advanced it is, the more basic the material it deals with.

 

[PrudensOptimus]

No, you can't learn Calculus on your own. You'll find out you were learning the wrong thing before you finish.

 

[phoenixthoth]

ok, most people can't. but some can.

 

[matt grime]

Given that the level we're talking about is no harder than find lineraizations, find tangent planes, find the partial derivatives of this (application rather thatn theory) it is not very demanding to teach yourself this - they are just simple formulae. We're not talking rigorous epsilon delta arguments, or an appreciation of sequential compactness

 

[Kalimaa23]

Originally posted by matt grime
We're not talking rigorous epsilon delta arguments, or an appreciation of sequential compactness

Excuse me? Are you suggesting that he'd just learn by heart some formulae? If you're going to do calculus, what's the point if you don't start of by the rigorous epsilon-delta formulation?

 

[matt grime]

Oh, I thoroughly agree, but the impression I get is that they're talking about '200 level or below' courses, which, translating into European parlance means they're doing very basic multivariable calc.

This is speaking as some one who's taught 200 level calc and had to wonder at the sheer lack of material in the course.

Imagine the level of maths we teach 16-18 yr olds (unless you're Russian in which case 12-13yr olds) but just with a couple more variables. No more than two/three obviously because then you can't appeal to pictures.

I think the text I taught from was by Finney, and is widely used in US universities for the first two years of calc. It does not contain many rigorous arguments that would satisfy a serious student of the subject.

 

[dmbeluke]

I need your advice and help. I've been out of school for over 10 years. Now I am taking Pre-Calc. I am trying so hard to understand and I spend a lot of my time trying to make sense of what I am trying to do. Is there a point when my mind will switch over into a different thinking process and truly grasp what I am doing? Is there any suggestions on what I can read to help me? Maybe a book called "Pre-Calc for the idiot?":) I want to eventually understand Physics and I need to know what I'm doing. I won't give up, but is there something out there to speak to me in a language I can understand until I get a hold on it? Any advice or direction will be deeply appriciated. Thank you.

 

[Kalimaa23]

Originally posted by matt grime
Oh, I thoroughly agree, but the impression I get is that they're talking about '200 level or below' courses, which, translating into European parlance means they're doing very basic multivariable calc.

This is speaking as some one who's taught 200 level calc and had to wonder at the sheer lack of material in the course.

Imagine the level of maths we teach 16-18 yr olds (unless you're Russian in which case 12-13yr olds) but just with a couple more variables. No more than two/three obviously because then you can't appeal to pictures.

I think the text I taught from was by Finney, and is widely used in US universities for the first two years of calc. It does not contain many rigorous arguments that would satisfy a serious student of the subject.

I'm in between the US and Russia. Here they teach rigorous calculus to 15-16 year olds.
Well, I suppose that's maybe overkill for many people, but then at least they have seen some math before they go to college.
I guess if you're only interested in applications, like economics or so, then maybe giving the results (total differential, chain rule, implicit function theorem) is sufficicient...

 

[Kalimaa23]

Originally posted by dmbeluke
I need your advice and help. I've been out of school for over 10 years. Now I am taking Pre-Calc. I am trying so hard to understand and I spend a lot of my time trying to make sense of what I am trying to do. Is there a point when my mind will switch over into a different thinking process and truly grasp what I am doing? Is there any suggestions on what I can read to help me? Maybe a book called "Pre-Calc for the idiot?":) I want to eventually understand Physics and I need to know what I'm doing. I won't give up, but is there something out there to speak to me in a language I can understand until I get a hold on it? Any advice or direction will be deeply appriciated. Thank you.

The only sure way to "get" mathematics is to spend time, a lot of time, on it. Persist and the light will come, no matter what books you use.

EDIT : maybe www.sosmath.com could be helpfull?

 

[dmbeluke]

Thank YOU for your suggestion- Dimitri T

You won't believe this- I understood what I was doing in class today! You were right- the time I am spending trying to "get" it is working. I am still going to check out that website you posted for me. Thanks again for taking the time to answer my ploy for help.
Dawn