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language more general than math Sure, some of us call it English. I can teach and understand many lessons from physics without diving into the math. What's hard to do is discover or prove physics without math. "A body at rest tends to stay at rest. A body in motion tends to stay in motion." I can throw tons of math at that but the idea can be ...


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There were two achievements of early humans and early civilization that led to us being able to state and understand the environment we lived in. One was writing, and one was math. Math started with counting, then adding, i.e. counting and arithmetic. Counting was invented very very early in the homo family by many different groups. Then arithmetic and math ...


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For any given physics problem, there will be an equation that describes the phenomenon that is being modeled. Whatever is varying in the problem will affect the phenomenon that you are interested in. The mathematical relationship between what is varying and the phenomenon of interest will determine whether or not the problem requires integration. To be ...


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1) How should one determine whether the problem at hand requires the use of calculus, in particular integration ? When the problem includes variations, we need calculus (integral and derivative). 2) Which variable or quantity should be made infinitesimally small? The variable(s) that variations of problem occur along it. In your case, the problem ...


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I think I found the proof for the Integral I mentioned, please verify whether my proof is correct or not $$\int\int f(\alpha)e^{\alpha^*y-z|\alpha|^2}\pi^{-1}~\mathrm d^2\alpha~=~z^{-1}f(z^{-1}y)$$ Proof: $$=\int f(\alpha)[\pi{-1}\int e^{\alpha^*{(y-z\alpha)}}~d\alpha^*]d\alpha$$ Using Identity $\pi{-1}\int e^{\beta{(a-b)}}~d\beta=\delta(a-b)$ $$=\int f(\...


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This is as far as I can get from the first two sentences: z-axis is the line perpendicular to dA.


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It doesn't come only on one side. Suppose I define a new pair of constants $K_1$ and $K_2$, which obey: $$R = \frac{K_1}{K_2}$$ Then I can write: $$K_2V=K_1I$$ And I have a constant on both sides. For convenience, we usually just collect any constant values into a single constant, give it a name, ideally an intuitive one, and put it on one side. Which ...


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No. $\frac{dT}{dt}$ is a variable whereas $k$ is a constant. Proportionality means that two quantities vary in the same ratio. If one varies but the other doesn't, they cannot be proportional.


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This functional analysis textbook is quite good, it even has a chapter dedicated on some of the mathematical foundations of quantum mechanics without using this name. This book is quite compact though, the classic text by Walter Rudin is more detailed. Prerequisites are topology and measure theory.


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Bayesian probability is based on the classical logic of plausible reasoning, as described by Jaynes, Probability Theory: The Logic of Science. One can and should try to find a Bayesian interpretation of the wave function. Here I can recommend Caticha's "entropic dynamics" as one possible approach. But I don't think "quantum logic" will be helpful here. ...


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Physicists do you the rules of calculus but can be sloppy in their notation. The symbols $\delta, \Delta$ and $d$ often seem to be used interchangeably to mean a (small or infinitesimal) change in something or better still a final value minus an initial value. So in your equation $dU$ is the change in internal energy of a system or final internal energy ...



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