#CALCULUS LEARN HOW TO#

However, the more important (and interesting) question is why you can compute integrals in terms of antiderivatives. A double integral is just the limit of this expression. Convince yourself that you can write the volume under a surface as a double sum. The reason why a double integral represents a volume is really the same. Convince yourself that you can estimate the area under a curve as a Riemann Sum:Ī 1-dimensional integral is just a limit of these sums. Understanding why an integral represents the area under a curve is actually fairly straightforward. Also things like why the product rule works and why we can find integration for volumes etc. But I still don't clearly know why integration over a certain region represents the area under the curve (for 2 dimensional x and y functions). For example I know why the derivative represents the slope (which in turn is the rate of change of one variable with respect to another) because I read up on the definition of the derivative and saw some examples. Instead what I'm looking for is an explanation of why we use what we use. Well I might have not been very clear in my OP but what I mean to say is that I don't really want an understanding touching on the deep, theoretical and axiomatic parts of Calculus. In time, you will be able to tackle more advanced topics like real analysis. You'll probably take a linear algebra course (which includes the formal axioms of vector spaces) and a discrete mathematics course (which will ease you into number theoretic and set theory stuff). If you are in a decent program, they will 'ease' you into formal mathematics. In time, you will learn to enjoy them!įor now, just enjoy your education. As a math major, you're not going to be able to escape these. All of them are axiomatic in nature and are fairly theoretical.

$calculus learn$

Many of the things that are bothering you will be answered if you carefully study these three subjects. You're going to need to study set theory, number theory, and most importantly, real analysis. You are not going to truly 'understand calculus' by reading calculus I/II textbooks. Half of the people out there follow equations blindly, while the other half are afraid to admit that they don't truly understand what is going on. You are suffering from something that should really be more common in our universities. 'In mathematics you don't understand things. So basically I need your help to guide me towards mathematical enlightenment. I am particularly interested in Calculus because I'm pretty confident about my conceptual understanding of the material learned before that. Any recommendations about what I should be doing to, what books to read or what sites etc I should be using would be extremely helpful. So I would like to start 'truly' learning what is all that stuff that I've been studying for some time now but I would like to do that without going over the baby steps students have to go through when they are learning these kinds of things for the first time (so I wouldn't wanna read a textbook).

#CALCULUS LEARN HOW TO#

It would be really sad if at the end of my major all I know is how to reduce something complex including all kinds of notations, variables and constants into something simple without really knowing what I have done.įurthermore, I've heard how hard a math major becomes for students who are good at solving for a number but when things like proof-writing start because they are no longer doing the kind of math they thought they were so good at. But the thing is, I don't really feel that I've actually truly 'learned' a lot of stuff I have studied, which is something that has been discomforting me lately, especially since I'm shooting for a math major.

Let's just say that I've done really well on any Math class I've ever taken and I've taken some rather advanced stuff for a first year college student. That is, I have no problems at all doing complex algebra problems or complex and tedious integrals and derivatives where there is little concept involved. Alright so I should start off by saying that I could be defined as the conventional 'math whiz'.

Calculus learn