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Results tagged with physics
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user 25510
For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.
25
votes
Motivation and physical interpretation of the Laplace transform
Besides the important physical motivation pointed out by Carlo Beenakker, there is another one, purely mathematical. Laplace transform is a generalization of a power series (and Dirichlet series).
In …
- 91.8k
6
votes
How does a Masters student of math learn physics by self?
Lifshitz, Course of theoretical physics, vol. I, and, of course,
V. Arnold, Mathematical methods of classical mechanics. …
- 91.8k
30
votes
Applications of complex exponential
The earliest application is the Mercator projection which was introduced long before the complex exponential was defined in the way we define it nowadays. $z\mapsto e^z$ is considered as a map from th …
- 91.8k
4
votes
Legendre equation: An interpretation
Now, this problem arises from problems of mathematical physics: to solve the Laplace equation in $R^3$, or to solve the eigenvalue problem for Laplace's equation. …
- 91.8k
17
votes
Accepted
Runner's High (Speed)
The constant is $2$. Let $n=\lfloor d_2/d_1 \rfloor \geq 1$, and let $t_k$ be the time which
the long distance runner takes to arrive at the distance $kd_1$ from the origin,
$1\leq k\leq n$.
Proving …
- 91.8k
2
votes
A particular contour integral
Carlo Beenakker's answer is right. When t>0, you cannot close the contour in the lower half-plane, because the exp
in the numerator is large in the lower half-plane. You must close the contour
in the …
- 91.8k
4
votes
A soft introduction to physics for mathematicians who don't know the first thing about physics
There are two outstanding books which I found very readable (I belong to the class
of mathematicians who have great difficulties reading physics books and papers):
Landau and Lifshitz, Mechanics, and …
7
votes
Deriving the Mercator projection algorithm
Most explanations miss a very simple point. Mercator projection becomes simple if
we use complex numbers.
It is the stereographic projection which sends the North pole to $\infty$
and the South pole t …
- 91.8k