Efficiently Mastering Calculus: Advice and Tips from a Student

[courtrigrad]

Hello all:

I am currently working through Richard Courant's Calculus. There are some problems which I just cannot do, either because it is extremely difficult or very time consuming. However, I have this obsession in wanting to do every single problem. Would it make more sense to move on to more important topics, read every chapter, and then do problems of your own liking? Do I have to do everything linearly? Is this a good way to study and master calculus?


Any advice is appreciated.

Thanks!

 

[HallsofIvy]

You shouldn't consider it necessary to do every problem. Courant, in particular, is a very deep text. It's much closer to "analysis" than calculus. The preface to the book, if I remember correctly, indicates which sections are necessary for sections later in the book. Failing that, remember that mathematics does depend upon what went before so, yes, you are better off doing "everything linearly".

 

[kdinser]

I used to do the same thing, obsess over not being able to do every problem.

While taking calc I and engineering physics I, I would get stuck on a problem. Sometimes, before I knew it, I would spend 3+ hours on the thing. I never really considered it a loss as I usually gained a deeper understanding of the material while working on it, but I know it cost me some points on tests because I wasn't as prepared for the whole chapter as I well as I should have been.

If you get stuck on one question, ask yourself this "have I been able to correctly solve similar problems?" "do I understand the nature of the problem and the concepts needed to solve it?" If the answers are yes, the thing that is probably giving you trouble is some simple algebra trick that you have forgotten or are just not seeing or maybe your setting it up wrong. If that's that case, do like I do, post the problem and your work to this forum and move on while waiting for an answer. Half the time I figure out what I'm doing wrong before I even post the problem. Just trying to explain something to someone else can really help jog your creativity and problem solving skills. But if all else fails, the people on this site know their stuff and are willing to help.