teaching myself calculus (for application in Physics)

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teaching myself calculus (for application in Physics)

Postby Yambert » Mon Aug 24, 2009 3:57 am UTC

soooo over the summer I taught myself a pretty wide range of alg/trig based physics, all of the topics on the AP exam plus a little bit of relativity and other Einstein things. This year I'm taking an AP physics class, that covers the aforementioned topics, but nothing on Calc/AP physics BC.

So I want to teach myself calculus based physics. How much Calculus do you really need to know for physics? For example I know you need relatively little algebra and trig for the physics I've already studied. Basically what I'm asking is, should I go all in and buy a calculus textbook, or will a calc-based physics book contain all of the calc I need?

For point of reference, I know nothing about Calculus, and I'm only interested in learning what I'll need to use for physics.
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Re: teaching myself calculus (for application in Physics)

Postby achan1058 » Mon Aug 24, 2009 6:12 am UTC

I don't know the details, but you probably don't need to buy a calculus textbook. They should either have the stuff in the physics text, or you can easily look them up anyways. There are enough free online sites that teaches basic calculus, including but not limited to MIT's Open Courseware.
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Re: teaching myself calculus (for application in Physics)

Postby Cup of Dirt » Mon Aug 24, 2009 6:49 am UTC

You probably just need to read the Wikipedia articles on limits, derivatives and integrals, in that order. Make sure you get the concepts, which very easy to understand, but don't worry about the formal mathematical details. I would say it would be a good start to understand the concepts, and then memorize the integrals and derivatives of a few elementary functions, like polynomials, trigonometric functions, and exponential functions. Then go ahead and try to do physics problems and see if you know enough. If not, you can always go back and read some more. The calculus you'll be required to do for the Physics AP exam is pretty elementary if I remember correctly, so someone with your motivation will probably have no trouble learning enough to get by in a pretty short amount of time.

Also, an integral table is very useful.
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Re: teaching myself calculus (for application in Physics)

Postby Minerva » Mon Aug 24, 2009 12:53 pm UTC

Make sure you're familiar with basic differentiation and integration, including in a straight mathematical context, but also in a physical context... eg. the relationships between position, velocity and acceleration.

From there, you need to be able to understand simple differential equations.

For some examples of applied calculus and basic DEs in real physics, can you derive Kepler's laws, starting from centripetal force, Newton's second law, and the Newtonian inverse-square gravity law?

If I told you that i\hbar\frac{\partial}{\partial t} \psi(x,\,t) = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2}\psi(x,\,t) + V(x)\psi(x,\,t) and that V(x) was equal to some potential, say an infinite one-dimensional square potential well, could you find a solution(s)?
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Re: teaching myself calculus (for application in Physics)

Postby You, sir, name? » Mon Aug 24, 2009 2:23 pm UTC

You'll probably need vector calculus at some point, since some problems (like electromagnetism) are not possible to reduce to a single dimension in a way that makes much sense.
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Re: teaching myself calculus (for application in Physics)

Postby megabnx » Mon Aug 24, 2009 5:13 pm UTC

While differential equations and multivariable calculus are nice to have for when you take college level physics classes and to help understand some formulas, they are in no way necessary for the AP. All questions are contrived in such a way where they will not be necessary. All you really need to know is the standard derivative identities, chain rule, integration=anti-differentiation, and *maybe* u-substitution. After that, AP physics is more a game of figuring out how to set up your equations than how to actually evaluate them.
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