Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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Convert time derivative to a function of time

Physics: I am asking for help to derive a general expression for the total amount of energy lost as a function of time from a radiating object. I'll simplify my problem like this: Say for example ...
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1answer
37 views

Finding moments $M_x$ and $M_y$ and center mass of a region

Set up integrals for the moments, $M_x$ and $M_y$, and the center of mass of the region (constant density, do not evaluate integrals) The region is a tall rectangle with a semi-circle on top. ...
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1answer
35 views

How does the hermitian conjugate of an unitary operator act?

I know that $$ A| v \rangle = \sum _n e^{i\alpha n} | n \rangle $$ where $A$ is an unitary operator, and $ \left \{ |n\rangle \right \} $ is an orthonormal complete basis. In that case, is it true ...
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1answer
81 views

Partial derivative with respect to metric tensor $\frac{\partial}{\partial{g_{kn}}}(g_{pj}g_{ql})$

$$-\frac{1}{4\mu_0}F^{pq}F^{jl} \frac{\partial}{\partial{g_{kn}}}(g_{pj}g_{ql})=+\frac{1}{4\mu_0} F^{pq} F^{lj} 2 \delta^k_p \delta^n_j g_{ql}$$ I need to know how to derive ...
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0answers
18 views

About diagonalizing a matrix for a quadratic expression (with the goal of uncoupling mixed terms)

my question is originated from a physical problem. I will try to present the problem as simple as possible, but I fear it will still be long since I'm bad at expressing myself briefly. It starts with ...
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1answer
36 views

Boyles law math problem [closed]

Let $$ P_1 = 1.37 atm \\ P_2 = 0.22 atm \\ V_1 = 1 L \\ $$ Boyle's Law says $$ P_1 * V_1 = P_2 * V_2 $$ What is the missing variable answer $V_2$? I'm having trouble.
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1answer
19 views

mathematical justification or creating a mathematical problem of the last part of a gauss theorem proof

this page proves the gauss theorem. First they prove that there has to be charge allocated in the origo of a function and that this is where you get the gauss formula and therefore you can integrate ...
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35 views

On the Name of the Amplituhedron

Shouldn't the 'amplituhedron' really be called an 'amplitutope' since it's really a polytope and not strictly a polyhedron?
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1answer
30 views

Displacement vectors

A rabbit trying to escape a fox runs north for 8.0m, darts northwest for 1.0m, then drops 1.0m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit? So I drew two ...
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2answers
31 views

Displacement vectors

You walk 53 m to the north, then turn 60 degrees to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east. So I did ...
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1answer
36 views

physical meaning of heat equation

consider the heat equation $u_t=a(t)u_{xx}+f(x,t)$, $0<x<L$, $0<t<T$ subject to the initial condition $u(x,0)=g(x)$ and boundary conditions $u(1,t)=0,$ $u_x(0,t)+hu(0,t)=0$ where ...
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23 views

How to move a body to a point using only velocity? [closed]

If I have two bodies, how can I move one of them at a constant velocity until it reaches the other's position? This is two dimensional x,y.
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1answer
25 views

Proving these are equal

We have the following equality (in physics) $$c^2t^2-x^2 = c^2t'^2-x'^2$$ where: $t' = \gamma (t- \dfrac{vx}{c^2})$ $x' = \gamma(x-vt)$ $\gamma = \dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}$ My ...
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0answers
14 views

Meaning of ideal membrane

I'm studying from a mathematical point of view the bidimensional vibrating membrane. How can I define an ideal membrane? What are the assumptions when I say 'ideal'? Thanks!
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2answers
32 views

From which equation of motion was this formula derived from in physics

When solving problems involving projectile motion I use: $\sqrt{2 * \dfrac{\text{height above ground}}{9.8}}$ Eg calculate the time it takes for a bomb to impact if it is travelling 4.9km above ...
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0answers
40 views

Launch angle required to hit coordinate (x,y) with air resistance

Finding Angle of Elevation to hit X, Y and Wikipedia Angle required to hit coordinate work, but don't calculate air resistance. Is there a way to find the launch angle of a projectile required to hit ...
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2answers
67 views

Separation of variables PDEs

In this answer, he has three cases $(\lambda = 0, \lambda \lt 0, \lambda \gt 0)$. I understand the first does imply it is linear, hence it isn't consistent with the initial conditions, and looking at ...
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1answer
61 views

PDEs for string deflection.

Okay, I have to find $u(x,t)$ for the string of length $L=\pi$ when $c^2=1$. I know: $$\text{wave equation}: \frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}$$ $$u(x,0)=\frac ...
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1answer
49 views

How to integrate Gravitational force?

The gravitational force is given by $$ F = \dfrac{-Gm_1m_2}{r^2} $$ But, since F = ma, then for an object placed at r distance away from the centre of the earth it would experience $$ a = ...
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1answer
30 views

Integrating the Schechter function…

I'm trying to integrate this equation over all L. I really have no idea where to start for some reason :S $$\phi(L)dL=\phi_0\left(\dfrac L{L\star}\right)^\alpha\exp\left(-\dfrac ...
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0answers
23 views

Momentum Representation vs Position Representation

I have a question involving the representation of operators in momentum representation and position representation. The question is a little long, so I'll do my best to explain it. We are given an ...
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1answer
38 views

Calculating the electric field of a disk

I'm having trouble regarding how to calculate the electric field of a disk. Here's the scheme: The exercise states that the disk is uniformely charged. This is what I did: Density charge : ...
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1answer
32 views

Finding the acceleration

So I am given a problem stated as: a point moves in the plane at speed 1 along the curve $y = x^2$. Find the acceleration at the point (x,y). I know that the velocity is y' = 2x, and that at a ...
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0answers
89 views

Rolling a ball into a cone; what should the forces overall be?

Suppose there is a cone, with the apex pointing down, and the top of the cone at height $h$, apex half-angle $\psi$, ball of mass $m$, and the initial velocity into the cone (completely horizontal, ...
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1answer
131 views

Guide to mathematical physics?

I am currently a math phd student specializing in algebraic geometry aspiring to work at the boundaries of the the fields of mathematics and physics and so, was looking into the field of mathematical ...
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1answer
137 views

Reference request: books that describe application of physical reasoning to mathematical problems

I am searching for more books like Uspenski's Some applications of mechanics to mathematics and Levi's The Mathematical Mechanic. In other words, I am looking for books that show interesting and ...
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1answer
21 views

What's the total of battery if 50mA of current are provided to a load for 1 hour?

What's the total charge that moves from one terminal of a battery to the other if 50mA of current are provided to a load for 1 hour? I think I'm suppose to use the formula I = Q/t, where I is the ...
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1answer
74 views

how to solve the system of differential equations for this particle?

I'm trying to solve this problem A particle of mass m moves under the action of gravity on the inner surface of a paraboloid of revolution $x^2+y^2=az$ which assumed frictionless. Obtain the ...
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0answers
21 views

Explain why we describe the flow of fluid passing through volume with this equation

I am new to this Q&A site. Recently I came across this expression while watching a video http://www.youtube.com/watch?v=GveJWPr9UOk/ about the mass of fluid flowing in through a cube. You can find ...
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1answer
62 views

Electromagnetism and thermodynamics(Statistical mechanics) books for the mathematician?

I found some very good classical and quantum mechanics,special relativity,gauge theory books for the mathematicians,but I couldn't find anything on electromagnetism or thermodynamics,are they of not ...
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4answers
54 views

Physical meaning of limit

Does the concept of "limit" have a well-defined physical meaning (like, for example, the derivative)?
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1answer
17 views

Regularity of the surface of a crystal

If I want to model the surface of any random crystal, is it safe to assume that it is the graph of a Lipschitz function. Is there a precise result from physicists? How wrong would it be if I assume ...
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2answers
77 views

Height and velocity of ball thrown vertically

A ball is thrown upward from roof of 32 foot building with velocity of $112$ ft/sec. The height after $t$ seconds is: $s(t)=32+112t-16t^2$. (a) Find the maximum height that the ball reaches. ...
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2answers
104 views

Set theory and physics [closed]

I would like to know if there are some physical concepts (preferably accessible ones like force, torque, ...) that can be significantly better understood when looked at in the light of concepts taken ...
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3answers
35 views

A silly question about potential functions

Why have physicists had the idea to define a potential function of a gradient vector field $\vec F$ to be a function $g$ such that $\vec F=-\nabla g$? What changes if we don't put the negative sign? I ...
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1answer
29 views

Simultaneous Suvat help [closed]

I learnt this in college but can't for the life of me remember how to do it. I've searched stack exchange and the internet for answers but it isn't clicking. It doesn't help my teacher has decided to ...
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3answers
76 views

Can someone check my work for this problem? Newton's second law of motion

At 560 metric tons, the airbus A-380 is the world's largest airliner. Whats the upward force on an A-380 when the plane is flying (a) at a constant altitude and (b) accelerating upward at 1.1 m/s^2 ...
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2answers
41 views

How far down will the ball travel and what is the magnitude of the ball's initial vector?

Confused a little with $V_x$ and $V_y$ components and how to find the displacement of X. A football is kicked with an initial velocity of $V_x = 30 \text{ ft/sec}$, and $V_y=80 \text{ ft/sec}$ 1) ...
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2answers
158 views

Problems in elementary number theory and methods from physics

I was wondering if there are intuitive "physical" arguments to solve problems from number theory (elementary number theory in particular, but also advanced topics). To make an example, a proof of ...
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1answer
54 views

Prove a=v*dv/dx

Using calculus, and assuming a particle moving along the x-axis is concerned, prove that $a=v*dv/dx$ ~~~~~~~~~~~~ this is what I did, but im not sure it's rigorous enough: $a=dv/dt$ $t=x/v$ ...
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7answers
2k views

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 ...
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1answer
35 views

Conversion problem

A cereal box says "net weight 340 grams" What's the actual weight (a) in SI units and (b) in ounces? What does net weight mean? Can I just go about this problem by simply converted the gram to SI ...
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2answers
22 views

Magnitude of Average Velocity

A train travels 100 miles toward 37 degrees northwest and then 90 miles north. The whole journey takes 2 hours. What is the magnitude of the average velocity of the train?
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1answer
54 views

Integral of voltage, $\int_{-a}^a \frac{dy}{\sqrt{x^2 + y^2}}$

This is (probably) a very easy integral to solve, but for some reason the answer just isn't coming to me (or at least the one my professor got isn't). He gave us a formula for voltage along the x-axis ...
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1answer
84 views

Electrostatic Potential Energy integral in spherical coordinates

I'm having trouble with evaluating an integral that arises from attempting to find the total energy of an electrostatic system consisting of two point charges, which involves an integral over all ...
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1answer
48 views

Show that requiring Electrostatic potential to be a stationary point of Electrostatic potential energy is equivalent to Laplace's equation.

Suppose we want to find the electrostatic potential $\phi$(r) inside of some volume $V$ with known boundary conditions. The physical field configuration should minimize the electrostatic potential ...
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45 views

Setting up an integral for a physics question.

The problem begins like this: a charge distribution is given by $\rho(r,\theta,\phi)=\gamma r^3cos\theta,a<r<b,0\le\theta<\pi/2$ and is zero everywhere else. The distance from the origin is ...
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1answer
113 views

Gradient and Laplacian in $S^1$

I'm trying to solve the particle in a ring problem without embedding the circle in $\Bbb R^3$, by instead taking the entire space to be $S^1$. Unfortunately, I haven't taken differential geometry yet ...
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1answer
33 views

Are the electric and magnetic fields functions on R^4?

Are the electric and magnetic fields functions from $\mathbb{R}^4$ to $\mathbb{R}^4$ (where $\mathbb{R}^4$ is then interpreted as space-time) or do we consider them to be functions from $\mathbb{R}^3$ ...
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2answers
326 views

Novel approaches to elementary number theory and abstract algebra

As a part of a university course, I'll have to study Herstein's Topics in algebra and Hardy&Wright's Introduction to the theory of numbers. Can you suggest some books (to be used as companions) ...