Physics Forums » Calculus
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Join experts in a discussion of calculus. Come across advanced integration techniques, ask questions about smooth infinitesimal analysis, and learn the slopes of curves. This may also include talking about other topics like Elementary functions, Calculating limits, derivatives, and integrals. The Physics forum is a community for students, scientists, educators, or hobbyists to learn and..
Physics Forums » Calculus
2d ago
I was trying to figure out how much landscape fabric I have left on a roll, given a known thickness ##T## of the fabric and the radius ##r## of that roll. I obviously don't want to do an integral to calculate it while I'm working, but was looking for some approximation that can be readily...
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Physics Forums » Calculus
6d ago
Hi,
I'm aware of the ##L^2## space of square integrable functions is an Hilbert space.
I believe the condition to be ##L^2## square-integrable actually refers to the notion of Lebesgue integral, i.e. a measurable space ##(X,\Sigma)## is tacitly understood. Using properties of Lebesgue integral...
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Physics Forums » Calculus
6d ago
Hello!
I considered number line and I couldn't take random points that correspond to hyperreal numbers on the hyperreal line. Instead it was points A, B, C that correspond to real numbers.
How to take random point that corresponds to hyperreal number on the hyperreal line?
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Physics Forums » Calculus
1w ago
The below proposition is from David C. Ullrich's "Complex Made Simple" (pages 264-265)
Proposition 14.5. Suppose ##D## is a bounded simply connected open set in the plane, and let ##\phi: D \rightarrow \mathbb{D}## be a conformal equivalence.
(i) If ##\zeta## is a simple boundary point of...
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Physics Forums » Calculus
3w ago
Quick two questions:
(a) In the hyperreals, is 0 considered an infinitesimal?
(b) Does a monad include the real number?
I seem to get contradictory answers in the Internet.
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Physics Forums » Calculus
3w ago
In calculating the integral ##\int{\ln\left(x\right)\,\sin\left(x\right)\,\cos\left(2\,x\right)}{\;\mathrm{d}x}##, I used a few online integral calculators to check my answer. According to one calculator, I got the correct antiderivative, but according to another (Math DF Integral...
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Physics Forums » Calculus
1M ago
Is the infinite series ##\sum_{n=1,3,5,...}^\infty \frac {1} {n^6}## somewhat related to the Riemann zeta function?The attached image suggest the value to be inverse of the co-efficient of the series.Is there any integral representation of the series from where the series can be evaluated...
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Physics Forums » Calculus
1M ago
Hello everyone, I've been brushing up on some calculus and had some new questions come to mind.
I notice that most proofs of the fundamental theorem of calculus (the one stating the derivative of the accumulation function of f is equal to f itself) only use a limit where the derivative is...
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Physics Forums » Calculus
1M ago
I’m having a little confusion about part b of this question as to why I am allowed to use the limit definition of a partial derivative.
Here’s what I think:
I know that y^3/(x^2+y^2) is undefined at the origin but it does approach 0 when it GETS CLOSE to the origin. So technically defining...
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Physics Forums » Calculus
1M ago
In free time I start to solve differentials and integrals, I am doing fine, I just follow rules and solve the tasks.
I start solve some applied calculus tasks, but I dont really understand why for exmple second derivative represent acceleration, why first is speed, why I need to derivate...
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