All Questions
Tagged with dimensional-analysis integration
10
questions
9
votes
4
answers
907
views
Can the differential be unitless while the variable have an unit in integration?
Apologies for terminology inconsistencies, as I'm reading a Chinese statistics and probabilities textbook while looking up intrinsics on an English encyclopedia.
This arose when I was reading the ...
- 211
0
votes
1
answer
78
views
Checking if an integral converges (or diverges) using dimensional analysis
I have been watching some online lectures in Physics, and the lecturer uses dimensional analysis to make claims such as the following:
Consider the integral
\begin{equation}
I(\xi, d) = \int_0^\xi \...
- 55
0
votes
0
answers
75
views
Euler–Maclaurin formula: Mismatched dimensions
To quote Wikipedia:
If ${\displaystyle m}$ and ${\displaystyle n}$ are natural numbers and ${\displaystyle f(x)}$ is a real or complex valued continuous function for real numbers ${\displaystyle x}$ ...
- 351
4
votes
2
answers
510
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Why are there factors of $2 \pi r$ in this volume integral?
I have a question regarding the solution to part of this homework question:
An infinite filled cylinder of radius $a$ contains a 3D charge density $\rho$. A thin-walled hollow cylinder of radius $b ...
- 419
0
votes
0
answers
359
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Show that $f:T^2 \rightarrow T^2$ is topological transitive
What is given:
Let K be a irrational number and $f:T^2 \rightarrow T^2$ be the homeomorphism of the 2-torus given by $f(x,y)=(x+K,x+y)$.
The exercise:
Show that for every non-empty, open, $f$-...
- 97
0
votes
1
answer
86
views
Theoretical/ Dimensional Analysis Question [duplicate]
Position is the integral of velocity.
However, position and velocity have different dimensions. How is this difference consistent with the conclusion that the integration sign is dimensionless?
5
votes
2
answers
147
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Dimensional Analyses in Integrals Producing Logarithms
Say I have equations of the form $f(x) = 1/x$ (to illustrate the simplest case of the problem) or $g(x) = \frac{1}{a - b \cdot x/c}$ and I want to find the integrals.
Normally, these would both be ...
0
votes
2
answers
72
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How to solve $f(x)$ in the equation $f(x)/F(x)=\ln(2)$ [closed]
I need to give one example of what $f(x)$ can be in the equation $\frac{f(x)}{F(x)}=\ln(2)$. $F(x)$ is the primitive function to $f(x)$. I need help to understand how to do that.
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1
vote
1
answer
618
views
Integral over Fractals with respect to fractal dimension
I understand that there is type of integral with respect to measures that can return values when evaluated over an integral. But is there an Integral that returns d dimensional volume where d is the ...
- 8,361
13
votes
1
answer
784
views
Why is an equation necessarily dimensionally correct?
I have just read a fascinating proof of the value of the integral $$ \int_{-\infty}^\infty e^{-ax^2} dx, $$ which proceeds by dimensional analysis, as follows: we know that we can write $$ \int_{-\...
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