How do you study calculus and retain the information you learn?

I'm taking my second calculus class this semester and I can't seem to remember anything from the first one, or to retain anything new. Math has never been my strongest subject, but I've always managed to do fairly well. I can't seem to do even that much now.



How do you study calculus? How do you retain the information from one math class to another, and when using it in other disciplines?How do you study calculus and retain the information you learn?Hello.



This is a very common question, and actually, in my opinion, it is rarely ever addressed properly.



The problem is that people try to study math like they would a history class. They try to memorize all of the formulas letter for letter and don't give it a second thought. This is obviously wrong (although, admittedly, this is a bad way to study history, as well) - math is NOT memorization - it is about problem solving. You take some concepts that you know and apply them generally to NEW problems and ideas.



So, you should understand the concepts behind what you are doing in class - you must understand what your formulas actually mean and decide how to apply them.



I'd really like to direct you to "Paul's Online Notes" (Paul, by the way, is a college professor). He has a little page on "How to Study Math". His discussion may be of more value to you than mine.



http://tutorial.math.lamar.edu/Extras/St鈥?/a>



Good luck to you.How do you study calculus and retain the information you learn?
Hey! I'm taking Calculus now too! =D



What I usually do is keep all my old notebooks and folders from my previous math class. This is because I know the next math class will build on the stuff we already know. It's hard to remember everything you learned last semester, or even last year so having the notebook to look back on is a great help.



For retaining new information I suggest doing practice math problems every night. That way the concepts you learn are always fresh in your mind. Even if there is no homework assigned for the day. Another thing you could do to study is to try to read over worksheets and book chapters. I also find that there are practice tests at the end of each chapter that you can use to study.



I hope I helped somewhat and I wish you good luck in your Calculus class!How do you study calculus and retain the information you learn?You have received a wealth of good constructive advice here, ranging from the purely pragmatic to the wonderfully esoteric... take it all to heart. May I point out, if you have not already realized it, that most calculus texts have answers to the odd-numbered questions and problem types that are similar often have similar numbering. Thus, picking a nearby odd-nmbered problem and checking your answer could potentially be a great help. Of course, make sure you understand every step in each sample problem of the section, and if necessary buy a student solutions manual and closely study solutions until you get in the swing of things... it is more than worth the effort! Calculus is beautiful regardless of whether it is the Calculus II you are taking or complex, real, Fourier, or nonstandard analysis.How do you study calculus and retain the information you learn?
Calculus is best remembered by using it to solve real world problems. Physics and P.Chem were a great help to me retaining what I learned in calculus. Math that we learn but don't apply is trivia to our brains. We quickly dump it to use that space for more important things.How do you study calculus and retain the information you learn?Just anytime you get a chance, and you notice a word that is unfamiliar or that you may have forgotten, just check it up online or in an old calculus textbook. Get into the habit of looking things up and calculus won't be so mysterious with hazy gaps anymore!
Practise, practise, practise.

Basically the same way you learned your "times" tables

Do all the exercises assigned, and then find some more!How do you study calculus and retain the information you learn?
repetition

do your homework

repetition

do extra problems

repetition

analyze the formulas and try to understand how and why they work

repetition
Calculus was Newton's sick attempt to one up the Al-Jabr. My advice? Boycott.How do you study calculus and retain the information you learn?
do the homework and listen to your teachers and TAs.
It is hard for me to conceive of why this is so difficult a question for me to answer; I fear I am obliged to ramble.



I would say you should focus on the derivations; if you know them well, the formulae will be harder to forget, while I don't think I am too different from most people in that I find forgetting comprehensible proofs impossible. As a practical matter, the important derivations to get right are the differentiation formulae. The Riemann sum arguments are a reflection of the higher-order-delta-cancellation arguments, but they take more notation to make work. Do a few of them to see how they are similar, but make sure you can derive all of the differentiation rules for the elementary functions. The derivations for things like integration by substitution or parts are easy-- of course parts is just the integral of both sides of the multiplication rule. Integration normally takes a bit more practice to get right than differentiation-- formally, integration of elementary functions by the traditional techniques is computationally undecidable because of the possibility of being snarled in infinite loops, according to a somewhat celebrated theorem of the 1960s as I recall. Computers integrate by using hypergeometric sequences, which arise when studying the series solutions of a famous differential equation studied by Gauss. I digress. Power series are frankly annoying unless you know complex analysis. I don't have a good suggestion for learning them other than learning complex analysis, which is a beautiful subject.



The limit laws are normally overdone in most calculus curricula out of guilt. They are obvious enough that you need not think about them much. The delta-epsilon argument, however, is surprisingly elegant and worth knowing intimately. The proof of the fundamental theorem of calculus is always a pleasure; it is short because it relies on the mean value theorem, which in turn is a trivial consequence of the intermediate value theorem. Few introductory calculus books bother to prove the intermediate value theorem, though an honourable exception is Michael Spivak's. This line of thought has to do with how continuity depends on the structure of the real numbers (calculus would not work well over the field of rational numbers). Considering the set of all functions, it turns out that infinitesimally few are actually continuous; the happy few which are themselves form a space (of an infinite number of dimensions, but not uncountably so); functions which take continuous functions into continuous functions, in turn may themselves be continuous: an example of such a function over functions is the differential operator. This infinite dimensional function space (Hilbert space or Banach space, after early 20th c. mathematicians) is in turn the basis for quantum mechanics: when we say a particle is a wave, we really mean it is an infinite dimensional vector, or a function which admits the usual calculus moves and a couple more stipulations (divergent integrals are not allowed because they imply infinite energy). You see the beginnings of this when you do power series expansions; each term in the power series may be seen as the function's length along a different axis.



To learn calculus, it is also worthwhile to have an historical sense for the history of mathematics. Newton developed calculus almost independently in three different ways: geometrically, algebraically, and with power series. Archimedes is believed to have had a great deal of Newton's calculus, perhaps up to but excluding power series, with the caveat that he probably saw it more from a geometric perspective. The algebraic formalism which dominates the modern curriculum obscures much of the intuition which allowed the calculus to be crystallised in formulae, but permitted the wonderful advances into differential equations of the eighteenth century, largely via power series and through a deeper and more general understanding of linearity.



I think I digress; this topic is perhaps too dear for me to treat well. Unlike other branches of higher mathematics, calculus is definition-light and formula-heavy. Instead of proof techniques, which are simple in calculus, what is more difficult are solution techniques. As others suggest, practice is important. Because of the very accretive nature of the calculus curriculum: differentiation, integration, power series, vector calculus, complex analysis, differential equations, partial differential equations, functional analysis, differential geometry, etc., (ignoring most of the modern analysis curriculum) and because all of these correspond to real physics problems, it is easy to get the requisite practice eventually, and no problem is difficult to visualise. I suppose in some sense I am telling you that calculus is easy instead of saying how to learn it, but I think my point is that the real problems which led to its development provide enough of an architecture to remember the solutions.



I hope you enjoy the calculus sequence; it is, if you will excuse the pun, a singular pleasure.



Best wishes--