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# Integrals? Fundamentals of Calculus?

guissmo
So, I'm approaching a time where I may fail my Math subject (I'm a Math major) due to the variety of hard problems our professor gives. Are there any people who would want to help me out by giving me Calculus questions (answerable by a freshman Math major - limits, derivatives, integrals and such)?

Xanatos
What math are you in currently? Because if you are having trouble with basic calculus I would suggest you rethink your major.
Afaceinthematrix
I agree with Xanatos. If you're a math major and you're having trouble with basic calculus, you either need to study your ass off or consider another major. How much do you know? It's hard for me to decide which problems to give you... Something to keep in mind: calculus is a combination of some easy and some hard problems all backed by extremely simple concepts. If you learn the concepts, then the problems get easy. For instance, do you know what differentiation is? Can you prove the limit definition to me and show me how a secant line becomes a tangent line? Learn all of the concepts and some of the proofs and it becomes easier. Here's some very basic problems to start with:

Lim (x--->0) (cosx)/x

F(x) = (x^2)(cosx)
F ' (x) = ?

Integral((lnx)/x)

If this is above your level and you haven't reached this yet, just tell me and I'll help you through it.
metalfreek
My major is Physics and calculus is a kind of Heart for Physics. I think a bit of practice and some memorization of formula is a big help in calculus.
Voodoocat
Afaceinthematrix is correct: if you don't understand why the formulas work, you will not be able to apply the formulas to physics. "Pattern matching math" might work for high school, but it will not get you through a physics major.

Try reading the explainations and proofs in your textbook, make notecards of the important details, and write the proofs. Then write the proofs and work problems EVERY DAY, 7 DAYS A WEEK for every concept and you should do fine. Sounds like a lot of work? Its physics and calculus, what do you expect
Afaceinthematrix
 metalfreek wrote: My major is Physics and calculus is a kind of Heart for Physics. I think a bit of practice and some memorization of formula is a big help in calculus.

Don't ever memorize anything in math! Learn to derive... Don't just "memorize the formulas." Understand the formulas.
Xanatos
 metalfreek wrote: My major is Physics and calculus is a kind of Heart for Physics. I think a bit of practice and some memorization of formula is a big help in calculus.

It is always much more useful for physics and math to ask why. Pure memorization may get you through right now, but you will need to understand the why later on. It is much better to get a head start than have to catch up later because you only memorized. If you understand the why much of calculus and physics will just sort of make sense.
metalfreek
What I ment about memorization was just formula. If you start to solve a question and you get
integration of (sinx) than would you start to derive that as well when you are trying to solve a much bigger problem. It is handy that you know integration of (sinx)= -cosx
Afaceinthematrix
 metalfreek wrote: What I ment about memorization was just formula. If you start to solve a question and you get integration of (sinx) than would you start to derive that as well when you are trying to solve a much bigger problem. It is handy that you know integration of (sinx)= -cosx

That still doesn't mean that you shouldn't know why. What if you forget? You should understand why something works and not just that it works...
metalfreek
You are right that we should understand how it comes. But while solving a bigger problems you need to know the basic things and formula. I find this way very handy and it saves a lot of time for me. I just memorize the basic formulas and go on with my work. I think I had to this because of the way I am taught and the way I give exams. In our system of Evaluation of students. He/She is required to appear in an examination which has a duration of 3 hours and you are not allowed to see any books or note and things like that. But you guys might have a open book exam and you dont have to rush to solve the question in a short time. But my system of evaluation force me to memorize some of the things.
goniagara
 Afaceinthematrix wrote: I agree with Xanatos. If you're a math major and you're having trouble with basic calculus, you either need to study your ass off or consider another major. How much do you know? It's hard for me to decide which problems to give you... Something to keep in mind: calculus is a combination of some easy and some hard problems all backed by extremely simple concepts. If you learn the concepts, then the problems get easy. For instance, do you know what differentiation is? Can you prove the limit definition to me and show me how a secant line becomes a tangent line? Learn all of the concepts and some of the proofs and it becomes easier. Here's some very basic problems to start with: Lim (x--->0) (cosx)/x F(x) = (x^2)(cosx) F ' (x) = ? Integral((lnx)/x) If this is above your level and you haven't reached this yet, just tell me and I'll help you through it.

True ... basic calculus should be easy for a math major, even a freshman. As an engineering student, I didn't start to lose it math-wise until partial differential equations