General calculus required for AP/college physics problems?

[Jewish_Vulcan]

I am supposed to take calculus next school year but I want to do some physics work over the summer. Can anyone provide me the the most common calculus problems in physics? I was thinking that derrivatives, integrals, limits, and infinate series would be the main ones but I am likely wrong.

 

[axmls]

Typically the first bit of calculus one sees in physics is in kinematics. Namely, the question of how to find a position function given a constant acceleration, knowing that acceleration is the second derivative of the displacement (with the velocity being the second derivative). After that, you can use calculus to find the work done by a varying force, it can be used in potential energy calculations (particularly when dealing with Newtonian gravitation). But I'm not so sure calculus is used that often in an introductory course in physics. It is used to prove certain things or to derive equations, but students typically don't see that many problems actually involving calculus. There are a lot of free body diagrams and energy calculations, but calculus only shows up in the less-than-ideal problems.

An example of its use to derive something is, for example, the position function given a constant acceleration. Given $$\frac{d^2 s}{dt^2} = a$$ and the initial values $s(0) = s_0$ and $s'(0) = v(0) = v_0$, we can integrate twice to get $$s = \frac{1}{2}at^2 + v_0 t + s_0$$ But this is merely to derive the formula, and unless you really hate memorizing formulas, it's not typically done more than once.

 

[RJLiberator]

Learn how to take a derivative inside and out.
Beyond basic derivatives and integration techniques you won't need much in a first semester physics course. It is of course, to your advantage to get a head and I suggest learning intimately the kinematic equations posted earlier and how they are derived. How the derivative of the position function is the velocity and the derivative of the velocity function is acceleration.

 

[alastairbrian]

RJLiberator Agree
Firest you have to start from derivation and integration, then move to more complex problems

 

[RJLiberator]

Yes. 100% agreed. To me, differentiation and integration is like the 'addition and subtraction' of calculus.