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1
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1answer
61 views

Integration by parts [closed]

Zee in his book, Quantum field in a nutshell mentioned the following, p. 22: Equation (14): $$Z=\int{D\phi}e^{i\int d^4x{ {\frac{1}{2}[(\partial \phi)^2-m^2\phi^2]+J\phi}} }$$ He said then, ...
1
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4answers
144 views

What is divergence?

What is divergence? I was learning about Maxwells equations and don't understand the divergence part of it. Can someone give an intuition of what divergence is in relation to maxwells equation. To ...
0
votes
0answers
21 views

Integration in the three coordinate systems [duplicate]

I need a book teaching triple and double integrations in the three coordinate systems and teaching vectors in three coordinate systems with no in depth mathematics. I need it to help me in general ...
4
votes
1answer
96 views

How is taking the average of an integral over an interval justified?

I have been studying classical mechanics. Often when going through a worked problem, I see a step where there is an integral from 0 to 2$\pi$ of $\sin^{2} \theta \ d\theta$. Instead of using the ...
3
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2answers
503 views

A basic math identity often used in integrals

I'm just wondering about why $y_i=A_{ij}x_j$ implies $$d^Ny=(\det A)d^Nx.$$ I see that $\det A$ is the product of the eigenvalues of a diagonal matrix but still don't exactly see how. Please help.
0
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0answers
22 views

Calculate static magnetic field in a volume of air with known sample points

So I know some calculus and I know some linear algebra, but do not really master electromagnetism (did a course ten years ago). There is a problem someone else has solved in a matlab script for me ...
2
votes
1answer
54 views

First variation of the action in relativistic notation - Landau & Lifshitz “Classical theory of fields”

In Landau & Lifshitz's book, Classical theory of fields, the action for a free particle is defined as: $$\tag{8.1} S= \int ^b _a {-mc \ \text d s}=0,$$ where $$\text d s=c\,\text d ...
3
votes
2answers
114 views

Why are some variables summed infinitesimally and others aren't?

This is something that has been bothering me and I hope the title kind of makes sense. It may be a stupid question but please be gentle. My question is, let's say we have current: $$I=\frac{dq}{dt}$$ ...
0
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2answers
61 views

Electric Field and Calculus: What is the physical significance of infinitesimal $dA$ in the equation of Gauss's Theorem?

In many equations we see infinitesimals $dA$, $dS$, $dx$ and so on. What is is the physical significance of these? Someone told me it signifies a small entity. For example,in case of $dA$ it signifies ...
10
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4answers
333 views

Electromagnetic field and continuous and differentiable vector fields

We have notions of derivative for a continuous and differentiable vector fields. The operations like curl,divergence etc. have well defined precise notions for these fields. We know electrostatic and ...
1
vote
1answer
80 views

Difficulty with the usage of Cauchy's integral formula in Griffiths QM book

On page 410 of Griffiths QM 2nd Ed. book, he begins an analysis to evaluate the integral: $$\frac{1}{2i}\int_{-\infty}^\infty \frac{s \sin{(sr)}}{(s-k)(s+k)}\mathrm{d}s.$$ To exploit Cauchy's formula, ...
1
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3answers
104 views

Integral ambiguity

I'm a bit confused with some notation I encounter in physics calculus. Consider this: Taken from here. Integration operates on functions, correct? What does it mean to integrate $\frac{d{\bf ...
1
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0answers
33 views

What is the relationship of the curl of a vector with its conservativeness? [closed]

My Physics teacher told me that a conservative field has zero curl.But I am not getting the logic behind it...I am even not clear why the curl represents how much the vector field swirls around the ...
0
votes
1answer
75 views

Landau's derivation of a free particle's kinetic energy- expansion of a function?

I was reading a bit of Landau and Lifshitz's Mechanics the other day and ran into the following part, where the authors are about to derive the kinetic energy of a free particle. They use the fact ...
-1
votes
1answer
54 views

Work to pump water through a hole in a trapezoidal prism

So I don't want to give the full details of the problem I'm working on, since I want to solve it myself. But I'm not sure which physical principles I'm supposed to use, since this is a Calc 2 ...
4
votes
4answers
629 views

Wrong calculation of work done on a spring, how is it wrong?

So I would have thought that this would be how you derive the work on a spring: basically the same way you do with gravity and other contexts, use $$W=\vec{F}\cdot \vec{x}.$$ If you displace a spring ...
0
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0answers
57 views

Finding the total space that an oscillating body has gone through via complex analysis

I was solving my homework and I got to an exercise that stated: An harmonic oscillating body has an equation of $$y(t) = A \sin(t)$$ Find the total space that the body has travelled during $t \in ...
1
vote
1answer
214 views

Inverse Fourier transform of Yukawa potential (troubles with Mathematica)

It can be proved that the potential $\frac{e^{-u|r|}}{|r|}$ has Fourier transform $\frac{4\pi}{u^2+q^2}$. Now, I'm trying to go backwards and do the inverse Fourier transform but I'm running into ...
0
votes
2answers
64 views

$R = dV/dI$ for varying temperature

I'm trying to do my prelab for an E&M course, and am asked if, for plotting $V$ vs $I$ with a varying temperature, I should expect a linear slope. I know that both $V$ and $I$ depend on $R$, and ...
3
votes
4answers
112 views

Based on note, how fast is a stringed instrument's string oscillating?

to be quite honest, I have no idea where to start on this problem mathematically. However, it struck my curiosity and would love to know how it works on a mathematical level. the problem You have a ...
0
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0answers
55 views

Integration of Forchheimer equation for unsteady-state permeability determination

I would like to know the steps for the integration of Equation 17 in Section 6.2.1.2 of American Petroleum Institute Recommended Practices 40 for Core Analysis to yield: ...
0
votes
1answer
51 views

Inconsistent integral and distance in spherical coordinates

I am currently studying this problem: 14 b) There you see an integral $$A(r) = \int f(\theta) (-\sin(\phi), \cos(\phi),0) d \Omega$$ where $f$ is the function containing all the rest of the integrand ...
2
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0answers
28 views

Book for multivariable calculus [duplicate]

Hi I want to start learning multi variable calculus specifically for learning electrodynamics. What are some good text books?
4
votes
1answer
117 views

Newton's original proof of gravitation for non-point-mass objects

Suppose we have two bodies, one very large (Earth), and one very small (a cannon ball). If the cannon ball is some distance away from the Earth, to find out the force produced on the cannot ball, we ...
3
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0answers
136 views

Heat transfer from hot water through a copper pipe to oil in a tank

I want to build a geyser attached to a pump with copper tubing running into an oil tank. This is done because the oil solidifies at a temperature below 15 degrees Celsius. I have done a few ...
1
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0answers
61 views

Applications of Calculus 2 to Physics [closed]

Im teaching a section of Calculus 2 (integration techniques, arc length, surface area, improper integrals, parametric & polar functions, sequences, and series ) next semester and would like to ...
0
votes
1answer
83 views

How to calculate average velocity

The position of an object moving along X-axis is given as $X=a+bt^2$ where $a=8.5\,\mathrm m$, $b=2.5\,\mathrm {m/s^2}$ and $t$ is measured in seconds. What is it's velocity at $t=0$ and $t=2.0$ s? ...
2
votes
4answers
613 views

Electric Field due to a disk of charge. (Problem in derivation)

This might be a really silly question, but I don't understand it. In finding the electric field due to a thin disk of charge, we use the known result of the field due to a ring of charge and then ...
2
votes
1answer
63 views

Taylor series expansion of $\ln$ and $\cosh$ in distance fallen in time $t$ equation

I want to find the Taylor expansion of $y=\frac {V_t^2}{g} \ln(\cosh(\frac{gt}{V_t}))$ I have tried using the fact $\cosh x= \frac {e^x}{2}$ for large t, which works, I just need help on small values ...
2
votes
4answers
97 views

Infinite series of derivatives of position when starting from rest

Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ...
0
votes
0answers
63 views

Ricci/Tensor Calculus and Matrix Calculus

What are the differences in the types of problems Ricci/Tensor Calculus and Matrix Calculus can solve? One formulation is generally used by the physics community and the other by statisticians and ...
0
votes
1answer
49 views

Movement with non-constant acceleration [duplicate]

Suppose we have a material point. If it is moving from position $X_0$ with initial velocity $V_0$ and constant acceleration $A$, then from elementary physics course I remember that its movement is ...
0
votes
3answers
154 views

Good math books for physicists [duplicate]

In his first lesson (transcripted in "Tips on Physics"), Feynman talks about math for physicists in a very cool and practical way. And at the end of the section he talks something like "so the first ...
0
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0answers
36 views

Is there any general position function $x(t)$ that gives the solution to $x''(t) = k/x(t)^2$, where k is a constant? [duplicate]

In physics class, I often come across various inverse square law equations like the following: $F_G= G\frac{m_1m_2}{r^2}$ $F_E = k_e\frac{q_1q_2}{r^2}$ Specifically, we are typically given ...
1
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2answers
47 views

If the net force on a current loop in a magnetic field is zero, why is torque independent of choice of origin?

Im trying to show that the integral over a closed loop of a crossproduct stays the same if I choose a different origin with $\overrightarrow{r}=\overrightarrow{r}\prime+\overrightarrow{r_0}$ and ...
4
votes
1answer
101 views

What's the proper interpretation of canceling infinitesimals? [duplicate]

In most textbooks of physics I've found this demonstration of work-kinetic energy theorem: $$\begin{align} W &= \int_{x_{1}}^{x_{2}} F(x)\ dx \tag{1}\\ &= \int_{x_{1}}^{x_{2}} m\cdot a\ dx ...
6
votes
4answers
397 views

Name this Mulltivariable Calculus Theorem

In Robert Wald's book General Relativity a multivariable calculus theorem is cited on page 16, which states: If $F:\mathbb{R}^n\mapsto \mathbb{R}$ is $C^{\infty}$ then for each $a=(a^1,...,a^n) \in ...
1
vote
2answers
112 views

Gauss' Law for Magnetism Derivative Form: With or without volume integral?

I've been reading through FLP Vol. II, and he has proven that as the flux through a closed surface is: $\ \int_{surface} \mathbf{F} \space \mathrm{d}\mathbf{a} $, according to the divergence theorem, ...
1
vote
0answers
107 views

How to calculate these integrals about propagator of QFT analytically?

How to get these three analytical solutions? Thanks very much! $$ G_{ret}(x,y) = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p \, \frac{e^{-ip(x-y)}}{(p_0+i\epsilon)^2 - \vec{p}^2 - m^2} = ...
3
votes
1answer
302 views

Three integrals in Peskin's Textbook

Peskin's QFT textbook 1.page 14 $$\int_0 ^\infty \mathrm{d}p\ p \sin px \ e^{-it\sqrt{p^2 +m^2}}$$ when $x^2\gg t^2$, how do I apply the method of stationary phase to get the book's answer. ...
1
vote
0answers
32 views

velocity function in slip effect

$$\frac{dp_l}{dx}-\mu_l\frac{\partial^2 u}{\partial y^2}=0$$ where $\mu_l$ and $p_l$ is the liquid phase viscosity and pressure, respectively; and $u$ is the flow velocity. The boundary ...
1
vote
1answer
64 views

Convective Operators: Cartesian vs Spherical Coordinates

(This question may be more appropriate for Math Stack Exchange, but since physicists tend to be more well acquainted with vector calculus, I'm asking the question here). This question is about ...
3
votes
2answers
390 views

Differentials in Spherical Shell - Maxwell Distribution

In explaining the Maxwell distribution of molecular speeds, my pchem textbook uses the following figure: We are basically trying to find the probability of having a particle with a speed $u$ between ...
0
votes
1answer
132 views

Why does the pure shear term / strain deviator tensor have non-zero entries on the main diagonal?

In a textbook of mine an operation is performed, of which I think the goal is to get zeros on the main diagonal of a matrix (the matrix represents strain). But im not sure that is the goal and Im also ...
0
votes
1answer
89 views

Trying to turn a nonlinear differential equation into a linear one

The problem I have today is to determine the differential equation for a square fin protruding from a wall that experiences surface to ambient radiation and has an internal heat generation of $\dot q$ ...
0
votes
3answers
158 views

Error propagation estimations for sine and cosine

My lab manual gives this: $B$ is a function of $A$, Greek are uncertainties... $$B + \beta = \sin(A + \alpha) = \sin(A)\cdot\cos(\alpha) + \sin(\alpha)\cdot\cos(A)$$ --> because $\alpha$ is ...
7
votes
1answer
226 views

Understanding Calculus Notation in Physics

I have just started a first-year calculus-based physics course about electromagnetism and waves. I am having trouble understanding what calculus notation means in the context of physics. Here is a ...
2
votes
3answers
213 views

Physical motivation for differentiation under the integral

I am thinking about the mathematical process of "differentiating underneath the integral", i.e. applying the theorem $$\partial_s \int_{-\infty}^\infty f(x,s)\,dx=\int_{-\infty}^\infty \partial_s ...
38
votes
6answers
2k views

How to treat differentials and infinitesimals?

In my Calculus class, my math teacher said that differentials such as $dx$ are not numbers, and should not be treated as such. In my physics class, it seems like we treat differentials exactly like ...
1
vote
2answers
161 views

Which of these two different forms of spin-orbit interaction is correct?

I am seeing the spin-orbit interaction in two different ways: $\lambda [\mathbf{p} \times \nabla V]\cdot \sigma$ $\lambda [\nabla V \times \mathbf{p}]\cdot \sigma$ I don't see how these two ...