Feynman Lectures on Physics Vol 2: Understanding "The Next Approximation

[jackiefrost]

I didn't want to overload the last topic, "The Meaning of Curl in Electrodynamics", but I have a question so I'll do it as a new thread.

I'm studying The Feynman Lectures on Physics - Vol 2, Sections 3-5 and 3-6: "The Circulation of a vector field" and "The circulation around a square:Stokes' Theorem". I've include a scan of these two sections at http://home.comcast.net/~perion_666/stuff/feynman1.jpg and http://home.comcast.net/~perion_666/stuff/feynman2.jpg .

In the second section, after eq. 3.33, Feynman says:

If we included the next approximation, it would involve terms in (delta y)^2 ...

My question is - what is "the next approximation" he's referring to. I don't see where any higher order terms like (delta y)^2 terms would come from in this analysis.

jf

 

[jtbell]

Equation 3.33 is basically a Taylor series, truncated at the linear term. For a function of one variable,

$$f(x) = f(x_0) + f'(x_0)(x - x_0) + \frac{1}{2} f''(x_0) (x - x_0)^2 + ...$$

For more than one variable, things get messier, but it's the same general idea.

 

[jackiefrost]

Ok, yes - I see it. I wasn't thinking about power series approximation. I guess he had to use that since he used a generalized form for the vector function C(x,y) , so C could be about anything. Thanks.

jf