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7 answers
20 votes
7k views
Using mathematics in theoretical physics
14 votes

First of all I strongly recommend a great two-volume book by R.Courant and D.Hilbert Methods of Mathematical Physics, vol.1 (linear algebra, series expansions, integral equations, calculus of ...

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4 answers
7 votes
5k views
Is it A Good Idea To Write Papers With Mathematica?
4 votes

There are a few books written in Mathematica and dealing with mathematical research (to some extent), they are really interesting, e.g. : "Mathematica in Action" by Stan Wagon (a ...

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3 answers
4 votes
9k views
What is a good differential equations textbook?
Accepted answer
4 votes

If you are looking for practical solving of differential equations I recommend : Advanced Mathematical Methods for Scientists and Engineers by Carl M. Bender and Steven A.Orszag. Methods of ...

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1 answers
1 votes
261 views
Functions satisfying differential equation of the Weierstrass elliptic function $\wp$
Accepted answer
3 votes

Given theorem on existence and uniquenes of solutions to ordinary differential equations (Picard's theorem) there is only one local solution if the Lipschitz condition is satisfied, in fact it is when ...

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1 answers
3 votes
155 views
Evaluating $I=\oint \frac{\cos(z)}{z(e^{z}-1)}dz$ along the unit circle
3 votes

This integral can be expressed with help of the residue theorem: $$I=\oint \frac{\cos(z)}{z(e^{z}-1)}dz=2\pi i \sum_{k}\; \mathrm{Res}(f,a_k)$$ There is only one removable singularity at $z=0$ and you ...

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2 answers
4 votes
2k views
Essay about the art and applications of differential equations?
3 votes

I strongly recommend to read a review paper with many interesting references therein : PDE as a Unified Subject by Sergiu Klainerman. An essay on partial differential equations written by a leading ...

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1 answers
2 votes
102 views
Compute the improper integral $\int_A \frac{dx dy dz}{(1+x^2z^2)(1+y^2z^2)}$ over an infinite cuboid
2 votes

It is more convenient to calculate the integral with respect to $z$ first and then with respect to $x$ and $y$. We have $$\int_{0}^{\infty}\frac{1}{(1+x^2 z^2)(1+y^2 z^2)} dz=\frac{x \operatorname{...

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3 answers
3 votes
3k views
Finding the values of the real constants such that the limit exists
2 votes

Method I Since we have a fraction going to a non-vanishing value given its denominator is going to 0 we have to assume that its numerator also tends to 0, therefore we should solve : Reduce[Limit[...

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2 answers
0 votes
86 views
Definite integral of the following question
1 votes

Let's write $$\int_0^\infty \frac{x \ln(x)}{x^4+4x^2+1}dx=\int_0^1\frac{x \ln(x)}{x^4+4x^2+1}dx+\int_1^\infty \frac{x \ln(x)}{x^4+4x^2+1}dx$$ For the first integral we change the variable $x\to z=1/x$ ...

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3 answers
0 votes
69 views
Difference of Roots Limit at Infinity
1 votes

$$\lim_{n\to \infty}(\sqrt{n^2+6b}-\sqrt{n^2-n})=\lim_{n\to \infty}\frac{n^2+6b-(n^2-n)}{\sqrt{n^2+6b}+\sqrt{n^2-n}}=\lim_{n\to \infty}\frac{6b+n}{\sqrt{n^2+6b}+\sqrt{n^2-n}}=\\ \lim_{n\to \infty}\...

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1 answers
1 votes
236 views
How to plot this problem? From Greek Exams
1 votes

Since there is no straightforward approach to plotting "curves" depending on three parameters one can use Manipulate with three controls. We have three complex numbers a0, a1, a2 but since they lie on ...

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2 answers
-1 votes
50 views
I'm having a problem interpreting and starting this problem with primes.
0 votes

Since $34 max(p,q,r)$ is even, it means that $p q + q r + r p$ must be even since $2018$ is even. Now, all three numbers of $p q, q r, r p$ cannot be odd, thus at least one is even, i.e. say $p=2$, ...

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