Calculus-Based Physics: How Much is Needed?

[GCT]

Although I have completed two semesters of basic physics, I'm going to need to take a calculus based physics course this spring. I am a bit concerned since it's been a while since I took calculus; does the course utilize calculus extensively (in terms of the amount of theorems one will have to know)...creatively (degree of manipulation of these theorems, one's familiarity with calculus)? I got a few more days before add/drop period ends.

 

[Pyrrhus]

Well if its General Physics, and not an specialized course, you will see polynomial integrals, in most cases, you need to know how to use the substituation method or perfect differential, also sometimes i did use Trig susbtitutions, you might want to review integration methods, and the derivatives formulas, mostly polynomial functions.

On Physics I, you won't see "hard" integrals as you did on your calculus courses, On Physics II, i did see some trigonometric integrals, and i did few trig substitution on the most difficult problems.
On Physics 3, you need to know line integrals and the gradient, maybe even more.

Ah i forget review the disk method and shells method, you will need it.

 

[jtbell]

I can speak only about the situation in the United States.

There's probably some variation from one college/university to another, but I think it's safe to say that most calculus-based introductory General Physics courses do not actually use a lot of calculus. If you understand the basic concept of the derivative and its connection to rates of change and the slope of a curve on a graph; and the basic concept of the integral as adding up a lot of little pieces, and its connection to the area under a curve on a graph; and can evaluate integrals and derivatives of simple functions like polynomials, trig and exponential functions, with simple substitutions, you'll do OK as far as pure math is concerned. Calculus is more important as a conceptual tool for writing down the basic laws of physics (e.g. velocity = dx/dt instead of simply distance/time).

It's been a while since I've taught that kind of course, because where I am now we have only an algebra-based General Physics course. Off the top of my head, the usual practical applications of calculus at that level include things like:

1. going from position to velocity to acceleration by taking derivatives

2. going from acceleration to velocity to position by integrating

3. calculating the center of mass and/or the moment of inertia of extended objects by integration

4. maybe calculating the electric field produced by an extended object, by integration

In the second semester, which is mostly electricity and magetism, you may use calculus in formulating Maxwell's Equations in either their differential or integral forms, but you won't do much in the way of actual calculations that involve grinding out integrals and derivatives.

 

[derekmohammed]

I don't know anything about the United states but if the course involves rotational movment, ossilations, or waves: THERE WILL BE TONS OF CALCULUS! (please excuse my enthiasm I love calculus) Also when you study anything on electricity there will be lots of calculus...

 

[GCT]

I'm slightly familiar with the application of calculus for 1,2 dimensional kinematics but have never even seen one relating to electricity, oscillations, roational etc...From the replies so far it seems that I've got some reviewing to do. Perhpas one of you can post an example of a basic differential calculus problem which requires a bit of "calculus creativity (referring to calculus functions, such as substitution)" or can refer me to a website.

 

[Gokul43201]

What exactly does your course entail ? Is it a mechanics course, or an electrodynamics course, or something else ? Do you know what is going to be covered in the course ?

 

[jtbell]

It would also help if you can tell us which school and which course; or if you don't want to get too specific, at least the country, and what kind of school it is. In the US, it makes a difference whether you go to an elite university, typical state university, engineering school, small private college, or local community college.

 

[jtbell]

On Physics 3, you need to know line integrals and the gradient, maybe even more.

You're thinking of the E&M stuff, right? Here, it probably varies depending on the course. As an example, I took General Physics at a small college in Ohio about 30 years ago. We used Halliday & Resnick, and were expected to already know basic calculus of one variable (differentiation and integration) but not multi-variable calculus. When we got to the E&M stuff, we were introduced to the concepts of line integrals and surface integrals. (Now that I think of it, we may have gotten line integrals when we studied work, earlier.)

But we didn't actually do any "real" line and surface integrals where you have to grind away at the mathematical machinery. We did only problems that were symmetric enough that we could evaluate the integral by inspecting a diagram. For example, if you have a sphere with a point charge at the center, the electric field E is uniform over the surface of the sphere, and is perpendicular to the surface of the sphere everywhere, so the integral of E over that surface is just k/r^2 (the uniform value of E) times the surface area of the sphere (4/3)*pi*r^2.

 

[GCT]

I believe at the most it will cover mechanics as well as electrodynamics, the course will probably cover the basics of physics. I will be transferring from Iowa to U of Georgia. I have forgotten all aspects of calculus except for simple differentiation, and a bit of integration; multivariable, surface, line integrals does not ring a bell. For the most part, I'll probably be able to handle it, but I imagine I'll drop by here a couple of times with unfamiliar subjects. Thanks for all of your replies.