Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [physics]

Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tag instead.

This tag is for questions on the mathematics required to solve problems in physics and should not be confused with those on physics concepts. Pure physics questions should go in the Physics Stack Exchange. For questions in the field of mathematical physics, please use the tag instead.

5372 questions
188
votes
9 answers

Importance of Representation Theory

Representation theory is a subject I want to like (it can be fun finding the representations of a group), but it's hard for me to see it as a subject that arises naturally or why it is important. I can think of two mathematical reasons for studying…
Eric O. Korman
  • 18,051
  • 3
  • 52
  • 82
141
votes
14 answers

Why do units (from physics) behave like numbers?

What are units (like meters $m$, seconds $s$, kilogram $kg$, …) from a mathematical point of view? I've made the observation that units "behave like numbers". For example, we can divide them (as in $m/s$, which is a unit of speed), and also square…
user377104
102
votes
19 answers

Good Physical Demonstrations of Abstract Mathematics

I like to use physical demonstrations when teaching mathematics (putting physics in the service of mathematics, for once, instead of the other way around), and it'd be great to get some more ideas to use. I'm looking for nontrivial ideas in abstract…
Jamie Banks
  • 12,214
  • 7
  • 34
  • 39
98
votes
10 answers

Why can't you add apples and oranges, but you can multiply and divide them?

What is the algebraic difference between arithmetic operations, that prevents entities with different units from being summed or subtracted, but allows them to be multiplied or divided? This looks more like a question for Physics, but lengths and…
danza
  • 1,153
  • 1
  • 9
  • 10
80
votes
9 answers

What is the meaning of the third derivative of a function at a point

(Originally asked on MO by AJAY.) What is the geometric, physical, or other meaning of the third derivative of a function at a point? If you have interesting things to say about the meaning of the first and second derivatives, please do so.
Gil Kalai
  • 1,073
  • 1
  • 14
  • 12
77
votes
10 answers

Is learning (theoretical) physics useful/important for a mathematician?

I'm starting to read The Princeton Companion to Mathematics, at the beginning it says: A proper appreciation of pure mathematics requires some knowledge of applied mathematics and theoretical physics. Some of my professors have told me that…
Vicfred
  • 2,724
  • 5
  • 25
  • 36
76
votes
4 answers

Teenager solves Newton dynamics problem - where is the paper?

From Ottawa Citizen (and all over, really): An Indian-born teenager has won a research award for solving a mathematical problem first posed by Sir Isaac Newton more than 300 years ago that has baffled mathematicians ever since. The solution…
jnm2
  • 3,040
  • 4
  • 21
  • 32
74
votes
8 answers

Very *mathematical* general physics book

I am searching for a book to study physics. So far, I've been suggested Resnick, Halliday, Krane, Physics, but it doesn't seem to be very suited for a math major. Can you suggest some more mathematical books? By mathematical I mean: rigorous,…
Dal
  • 7,726
  • 5
  • 38
  • 94
62
votes
15 answers

Why learn to solve differential equations when computers can do it?

I'm getting started learning engineering math. I'm really interested in physics especially quantum mechanics, and I'm coming from a strong CS background. One question is haunting me. Why do I need to learn to do complex math operations on paper…
user60462
  • 823
  • 1
  • 7
  • 8
53
votes
2 answers

Xmas Maths 2015

Simplify the expression below into a seasonal greeting using commonly-used symbols in commonly-used formulas in maths and physics. Colours are purely…
Hypergeometricx
  • 21,842
  • 2
  • 25
  • 82
45
votes
7 answers

Dirac Delta Function of a Function

I'm trying to show that $$\delta\big(f(x)\big) = \sum_{i}\frac{\delta(x-a_{i})}{\left|{\frac{df}{dx}(a_{i})}\right|}$$ Where $a_{i}$ are the roots of the function $f(x)$. I've tried to proceed by using a dummy function $g(x)$ and carrying…
The Wind-Up Bird
  • 701
  • 1
  • 6
  • 8
45
votes
3 answers

Intuitive reasoning behind $\pi$'s appearance in bouncing balls.

This video is about an interesting math/physics problem that when cranked out churns out digits of $\pi$. Is there an intuitive reason that $\pi$ is showing up instead of some other funky number like $e$ or $\phi$, and how can one predict without…
picakhu
  • 4,840
  • 1
  • 27
  • 57
43
votes
17 answers

What is a simple, physical situation where complex numbers emerge naturally?

I'm trying to teach middle schoolers about the emergence of complex numbers and I want to motivate this organically. By this, I mean some sort of real world problem that people were trying to solve that led them to realize that we needed to extend…
Joshua Frank
  • 635
  • 5
  • 8
41
votes
2 answers

Physicists, not mathematicians, can multiply both sides with $dx$ - why?

The following question is asked without malicious intentions - it's not intended as a flamebait! In my physics textbooks (Young & Freedman in particular) I have often seen derivations of equations that use multiplication of, say, $dx$ on both sides,…
trolle3000
  • 967
  • 2
  • 12
  • 18
40
votes
3 answers

reference for multidimensional gaussian integral

I was reading on Wikipedia in this article about the n-dimensional and functional generalization of the Gaussian integral. In particular, I would like to understand how the following equations are derived: $$ \begin{eqnarray} & {} \quad \int…
harlekin
  • 8,060
  • 5
  • 34
  • 70
1
2 3
…
99 100