How to use derivatives and integrals

[winston2020]

I'm in University Physics, and my prof. just gave us a lecture to make sure we're aware of how to use derivatives and integrals (first year). However, I haven't learned integrals in high school, and all this quick review did was confuse me.

Would someone kindly take a few minutes to give me a quick summary of how integrals work (as well as the notation, which looks like greek [and probably is :P])?

I know that they are used to calculate the area under a curve given a certain interval. The concept is not the problem, it's the actual application.

 

[NoMoreExams]

You should probably drop your class and take calculus first (you should have a list of prereqs for your physics class, have you fulfilled them?) or at least take them concurrently. I don't think you truly want someone to summarize Calc 1 and 2 in a post do you?

 

[winston2020]

You should probably drop your class and take calculus first (you should have a list of prereqs for your physics class, have you fulfilled them?) or at least take them concurrently. I don't think you truly want someone to summarize Calc 1 and 2 in a post do you?

I'm currently taking Calculus. I have the pre-requisites for my course. The issue is that the high school math curriculum has recently changed, and no longer includes integrals. I will learn them this semester in my math course, but I need them in physics right now.

I do know derivatives however, just not integrals.

 

[ice109]

don't worry they won't be used anywhere in your physics class

 

[winston2020]

don't worry they won't be used anywhere in your physics class

I don't see how you've come to that conclusion.

 

[Defennder]

don't worry they won't be used anywhere in your physics class

? They are used everywhere in 1st year physics classes. For example, work done by a force along a path is a line integral but in first year, that usually reduces to a single variable integral. If he doesn't know integration, how is he going to be able to understand or apply the concept here?

Anyway, I'm just surprised that your high school didn't cover integration at all. You definitely have to do at least calc 1 before doing that physics class.

 

[madmike159]

I'm suprised they let you on the course at all.

 

[winston2020]

It's nothing to do with me; even my professors and TAs have said it's a problem with the high school curriculum. They no longer sufficiently prepare students for university... one of the most lacking subjects apparently is math.

With that said, thank you all for your advice. I am enrolled in calc1 right now, but until we cover integrals, I'll read ahead in the book, and post any questions I have.

Thanks again :)

 

[epenguin]

? They are used everywhere in 1st year physics classes. For example, work done by a force along a path is a line integral but in first year, that usually reduces to a single variable integral. If he doesn't know integration, how is he going to be able to understand or apply the concept here?

It may be a slight handicap to have not gone through that rigmarole, but it is a thing everyone forgets after a year. For following all the arguments in a physics textbook it is not necessary. Don't worry how they integrated a thing, just check that the answer is right. It is the inverse of differentiation so you know how to do that. (Which your classmates should do as well but won't as they will be worn out by the effort of the pesky integration). And there are hand calculators as well as computer programmes that can handle most things.You have to know what it means of course, what definite and indefinite are and enough to not be flummoxed when e.g. you see multiple integrals.

I know I am a bit of a subversive on this and not traditional so expect to see mostly contrary opinion.

(One of the nicest things I remember a teacher saying about me in class at school was 'He isn't clever - just a master of low cunning! pride:rofl:)

 

[Defennder]

Well, integration is so fundamental to everything in physics I really don't see how the OP can make it through without knowing it in advance. For example, he said earlier that he doesn't even recognise the integration sign at all. Secondly, it's not just to read and understand the textbook that he'll need knowledge of integration for. I did a 1st yr physics course in my first semester and came across a question (given online as part of homework) which required me to integrate to find the work done to move a block across two sheets of material with different coefficients of kinetic friction. This is an example where knowledge of integration itself isn't enough, you also need to combine it with how to apply it in physics to solve such problems.

 

[madmike159]

And there are hand calculators as well as computer programmes that can handle most things.

Try microsoft maths, its very good and does calculus, algebra and more complicated stuff like imaginary/complex numbers.

 

[poonlam]

integral is actually the opposite of derrivative.
ex: the derrivative of x square is 2x.
then the integral of 2x is x square.

 

[madmike159]

integral is actually the opposite of derrivative.
ex: the derrivative of x square is 2x.
then the integral of 2x is x square.

No. The integral of 2x (WRt x) is x^2+c.

 

[poonlam]

No. The integral of 2x (WRt x) is x^2+c.

oh yah i forgot. sr.

 

[madmike159]

Try microsoft maths, its very good and does calculus, algebra and more complicated stuff like imaginary/complex numbers.

Also I might add I have the Casio fx-991ES calculator, which is very good. It does intergration and differentiation, logs (any base), all the usual stuff, matrices, vectors, different base number conversions solving equations, stats and tables and complex numbers. It also has 40 conversions and 40 constants built in. Its a very usful tool for any maths or science lesson.

 

[poonlam]

you can use TI calculator too. I am using TI 84 right now. its like $163. though I am not sure if colleges allowed us to use calculator during test or not.

 

[madmike159]

$163 sounds like quite alot, although the ability to do graphs is very usful. Mine was £16, which is about $28-29.

 

[poonlam]

$163 sounds like quite alot, although the ability to do graphs is very usful. Mine was £16, which is about $28-29.

dude its hella cheap. idk why mine is so expensive... but my teacher recommends us that calculator. so yah, i have to buy it anyway!

 

[madmike159]

The best thing to do is get the second best. The model below my calculator is £6 ($11).
There is also a really good one I've seen for £80 ($147). http://www.casio.co.uk/Products/Calculators/Graphical%20Calculators/FX-9860GSD-LB-EH/Technical_Specifications/
Although the TI 84 looks better.

 

[Troponin]

Find a list of basic integrals online and study it until you have it memorized.

Just remember that the integral is the anti-derivative...in many physics problems that will be enough to get you what you need.

If you have time to learn any integration techniques, I'd recommend getting an idea of substitution (often called u-substitution) and integration by parts. Just a basic understanding of how they work should probably get you through most of your sticking points.

If the professor sees that this is a continuing problem, the work is probably set up so as not to include many difficult integrals, so a basic understanding that they're just the anti-derivative will probably be enough to scrape by.