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Zee just wants to distinguish the integration $\int \mathrm{d}^4x$ from the integration $\int \mathcal{D}\phi$ when calling this "integration by parts under $\int \mathrm{d}^4x$". As for how the integration by parts itself works, observe that, for any function $f$ vanishing at $\pm\infty$: $$ \int f'(x)f'(x)\mathrm{d}x = f(x)f'(x)\rvert^\infty_{-\infty} - ...


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in w=F.X, x is displacement of center of mass of the body not the displacement of system. here also force is 'kx' and displacement of c.o.m. is 0.5*x,so work done will be 0.5kx^2.


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Here's a derivative-free explanation. For readers who are doing E&M at the college level, the other answers posted here are more comprehensive, but since the OP has stated a high-school knowledge with little math and physics knowledge, here's the primer: A vector is a quantity that, in order to be fully measured and described, needs to include both a ...


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The two maxwell equations using divergence are $$ div \vec{D} = \rho \\ div \vec{B} = 0 $$ at least in differential form. In integral form they are maybe more clearer for you. They are $$ \iint_{\partial V} \vec{D} \ d \vec{A} = \iiint_{V} \rho \ dV = Q(V) \\ \iint_{\partial V} \vec{B} \ d \vec{A} = 0$$ The first equation just means the electrical flux $D$ ...


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Taking your (lack of) knowledge about differential geometry into account, this might be too hard to follow, but here it goes anyway: Let $u_1,\dots,u_n$ be some tangent vectors with base point $p$ and $\omega$ the volume form, ie $V = \omega_p(u_1,\dots,u_n)$ is the (possibly negative) volume of the parallelepiped spanned by these vectors. In case of three ...


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Divergence is an operation that maps a vector field $\vec D(x,y,z)$ to a scalar field ${\rm div}\,\vec D(x,y,z)$. How do you calculate ${\rm div}\,\vec D(x,y,z)$? Either you follow the definitions using derivatives, which you can't if you don't know what a derivative is. Or you imagine the following: the vector field $\vec D(x,y,z)$ tells you about the ...


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Meaning, why can't this exist: $dI=\frac{dq}{dt}$ Is this a calculus question? Or is this just by the definition of current? It can exist, and I would consider this a calculus question. When Newton and Leibniz originally invented calculus, they conceived of a derivative as a (usually finite) ratio of two infinitesimal numbers. Infinitesimal ...



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