3,561 reputation
1137
bio website lightandmatter.com
location
age
visits member for 3 years, 4 months
seen Sep 30 at 23:43

I teach physics at Fullerton College, a community college in Southern California.


Sep
24
awarded  Autobiographer
Aug
18
awarded  Popular Question
Aug
4
comment In calculus, which questions can the naive ask that the learned cannot answer?
+1, but I don't think a naive first-year calc student would be at all likely to come up with this series. It takes a lot of insight to understand why its convergence is difficult to establish, and why the exponents 3 and 2 work.
Aug
3
revised Intuitive explanation of the difference between waves in odd and even dimensions
Kevin Brown is the mathpages guy, not John Baez
Jul
26
comment Could we assign a numerical value to an infinitesimal?
I don't understand the point of the question. When I first read it, I thought maybe you were trying to reinvent the wheel, and you just needed to be told about the existence of systems such as non-standard analysis (NSA) and smooth infinitesimal analysis (SIA). But then I saw in one of your comments that you had already heard about SIA. So what is this question asking? Are you proposing a third system and asking whether it's useful or consistent?
Jul
26
comment What are some conceptualizations that work in mathematics but are not strictly true?
@EricLippert: Symbols like $dy$ and $dx$ can be defined as infinitesimal numbers. That's historically what they originally meant, and there's nothing wrong with it. See math.stackexchange.com/questions/21199/…
Jul
22
awarded  Yearling
Jul
20
comment Why is $\sin(d\Phi) = d\Phi$ where $d\Phi$ is very small?
@jpmc26: The foundational aspects of calculus have gone through a series of changes over the centuries, and therefore different people have different ideas about the meaning of a symbol such as $d\Phi$. The original meaning was that it was an infinitesimal number. That fell out of favor ca. 1850-1960, when the foundations of calculus were rebuilt in terms of limits. Then infinitesimals, which scientists and engineers had never stopped using, were rehabilitated. A nice book on this topic at the undergraduate level is Keisler, math.wisc.edu/~keisler/calc.html
Jul
14
awarded  Popular Question
Jul
13
comment Formalizing Those Readings of Leibniz Notation that Don't Appeal to Infinitesimals/Differentials
Related: math.stackexchange.com/questions/865559/… . I think the basic issue you're running into is that Leibniz notation predates the notion of a function by a couple of hundred years. Leibniz and his contemporaries thought in terms of expressions, not functions, and the notation implements that attitude.
Jul
12
asked Modern notational alternatives for the indefinite integral?
Jul
12
comment Calculus with leibniz notation
You may be interested in this book by Keisler: math.wisc.edu/~keisler/calc.html
Jul
10
comment Best applications-oriented introductory calculus textbooks?
Agnew may actually be public domain now. Its copyright was in 1962, and it doesn't appear to have been renewed.
Jul
2
awarded  Curious
Jun
24
revised Standard terminology for infinite limits with opposite sign on the two sides?
added 265 characters in body
Jun
24
comment Standard terminology for infinite limits with opposite sign on the two sides?
@Omnomnomnom: I should have specified: it is sometimes the case that it would be considered wrong to say that the first limit does not exist OK, if the terminology is not totally standardized then that would be good to know. However, in the small sample of books I have handy on paper or online, all seem to define the first limit as not existing.
Jun
23
comment Standard terminology for infinite limits with opposite sign on the two sides?
@mm-aops: So how would you distinguish the two cases in the question? #1 "has an infinite limit," while #2 "has no finite or infinite limit?"
Jun
23
comment Standard terminology for infinite limits with opposite sign on the two sides?
We talk about "lateral limits". The limit with "+" is the limit from the right, and the other is the limit from the left. Yes, I understand that. One could certainly describe them as "a limit that is infinite and has the same sign from both sides" versus "a limit that is infinite and has opposite signs from the two sides." However, that would be very cumbersome.
Jun
23
comment Standard terminology for infinite limits with opposite sign on the two sides?
@TomCruise: Are you saying you'd describe the second limit as existing but not converging? AFAICT from looking at various sources, that would be nonstandard.
Jun
23
comment Standard terminology for infinite limits with opposite sign on the two sides?
@Omnomnomnom: As far as I can tell by looking at various sources, people describe both of these limits verbally as not existing. I'm asking for a verbalism that distinguishes the two cases.