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How to show the Hamiltonian is conserved
I have the langrangian $L = \frac 1 2m((1+4r^2)r’^2) + \frac 1 2 mr^2 θ’^2 -mgr^2 $ I worked out theHamiltonian and 4 Hamiltonian equations and got $\frac...
Apr 20, 2026
Archive: News
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Difference between Integral Domains and Fields.
Can someone please help me in figuring out how all fields are integral domains but not all ID are fields? My course assumes IDs to be commutative with uni...
Apr 20, 2026
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What is a maximal abelian extension of a number field and what does its Galois group look like?
How does one know that a number field $K$ has a maximal abelian extension (unique up to isomorphism) $K^{\text{ab}}$? I've read proofs involving Zorn...
Apr 20, 2026
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Converting from Cartesian coordinates to Spherical coordinates
I want to understand how to convert from Cartesian coordinates to spherical coordinates. I have the following definitions: \begin{align} x & =r\sin\th...
Apr 20, 2026
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Integer Solutions for linear equation
What are the different methods for solving a linear equation with integral Solutions? Which one is preferred over other? What is the best method? For exam...
Apr 20, 2026
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Is there a symbol for the number of dimensions in a vector?
Here's an equation from a text book for computing a unit vector: $$\hat v = \frac{\overline v}{ \sqrt{ \sum ^n _{i=1} (\overline v_i)^2 } }$$ Now I m...
Apr 20, 2026
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When two segments between two parallel lines have the same length, are they always parallel?
This seems like such an elemental thing to me, but I don't want to assume it's always true, since there could be an exception. Also, without kno...
Apr 20, 2026
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domain of composite function (is there a set rule)
In the function topic of "function combinations" or "function algebra", for the basic arithmetic operations of the following: 1) f + g 2) f - g 3) f * g 4...
Apr 20, 2026
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A three-character password, how many different passwords are possible?
a three-character password consists of 2 different digits between 0 and 9 inclusive. and 1 letter of the English alphabet. the letter must appear as first...
Apr 20, 2026
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What does the letter U mean in math?
What does the letter U mean in the following expression: $$ \bigcup_{\alpha} A_\alpha \;? $$ It doesn't look like logical OR. Link to original screen...
Apr 20, 2026
