Learning Calculus: Intuitive & Physical Approach

[relativelyslow]

i am looking to learn calculus. i will take it in college for i wish to major in physics but i thought it would be helpful to learn it now, plus i think it will help with my independent physics reading and whatnot. i also think it will be cool in itself. anyways, i am considering getting calculus: an intuitive and physical approach by morris kline. i really only know what I've read from reviews, although i did read a wee in barnes and noble. does anyone have any experience with it? i was thinking if i needed assistance with it i could also use calculus made easy from the good old library. any suggestions or recommendations? thanks

 

[Hurkyl]

I can't help you with books, but I do have a piece of advice that you might not have considered -- strengthening your algebra skills may (or may not) prove more useful than getting an early introduction to calculus. Of course, I can't recommend anything for that either, so I'm not much help, sorry.

 

[Chrono]

I can't help you with books, but I do have a piece of advice that you might not have considered -- strengthening your algebra skills may (or may not) prove more useful than getting an early introduction to calculus.

That's good advice there. Taking calculus has even enhanced my algebra skills since I started taking it.

There are a couple of sites out there that can make worksheets for you. Math.com is a good one for algebra.

 

[fliptomato]

i am looking to learn calculus. i will take it in college for i wish to major in physics but i thought it would be helpful to learn it now, plus i think it will help with my independent physics reading and whatnot. i also think it will be cool in itself. anyways, i am considering getting calculus: an intuitive and physical approach by morris kline. i really only know what I've read from reviews, although i did read a wee in barnes and noble. does anyone have any experience with it? i was thinking if i needed assistance with it i could also use calculus made easy from the good old library. any suggestions or recommendations? thanks

Greetings RS--kudos on your initiative. I'm a junior in a university and majoring in physics, and the one piece of advice I cannot over emphasize is that textbooks are like clothes: you have to find the ones that fit you. Don't be surprised that even if you're assigned one textbook in a class, you'll find it much more helpful to reference many other books in the library.

There are several standardized calculus texts out there--you could even look up whatever textbook they're using at the local college. For the most part, you should be fine picking up an older edition from the library (intro calc hasn't changed all that much in the past hundred years or so). You might even be able to find good tutorials online. (Check, for example, this site.)

That all being said, here are a couple of my favorites:

• . This is one of the classics--it may be a little advanced, but it gives good insight.
• . I believe this is the text used in Stanford's single-variable calculus sequence; I've found it a good reference.

Flip

 

[relativelyslow]

im not sure those two are in my library but ill check. i wouldn't really want to buy them because, being textbooks, they are quite expensive. i do have the textbook for the calculus class i was initially enrolled in this year for she has not requested it back, hopefully as it will stay (i did, as most others did, drop the class because i was not learning anything). what was intriguing to me about morris klines book, at least what i gathered from the reviews at amazon, was that he explains why things are done and their application. i think it is more important, at least in the beginning, to know why rather than how (or the two paired together). i always imagined textbooks as machine like- giving cold equations and problems to do with no necessary understanding. perhaps, as it appears to be, i am wrong. thanks for your input so far, i appreciate it.

 

[Calgria]

Make sure you have your algebra and trig down. The calculus concepts are relatively simple, just applying the algebra and trig to them is where I make many mistakes.

 

[jtbell]

strengthening your algebra skills may (or may not) prove more useful than getting an early introduction to calculus.

I don't know what it's like elsewhere, but many or most of our students seem to have learned algebra only in the context of equations that have one variable and numeric coefficients. They can take an equation like

$$4 = \sqrt{x^2 - 5}$$

and solve it for $$x$$, but if you give them something like

$$E = \sqrt{p^2 c^2 + m^2 c^4}$$

and ask them to solve it for $$p$$, they look puzzled and say something like, "what do you mean? there aren't any numbers!" I have to explain to them that I want them to get an equation that has $$p$$ all by itself on one side. They simply haven't done that kind of thing in their math classes!

Similarly, when you give them an equation like the one above, and numeric values for $$E$$, $$m$$ and $$c$$, and ask them for $$p$$, they plug in the numbers immediately and then solve for $$p$$, rounding the numbers off as they do each arithmetic step and getting significant errors in their answers. I have to take off points repeatedly for this in order to get them to do the algebra first, then plug in the numbers and calculate the answer in one continuous sequence on their calculators, without significant roundoff error.