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comment Demonstrate the convergence of an integral
Hint: Switch the order of integration...
Aug
23
comment Does anyone use the notation $\mathrm d^3(x,y,z)$?
The notation in physics which I know is $d^3 r$ to distinguish it from $dr$. One would associate at vectorial character with $d^3 \mathbf r$ (similar to the line element $d \mathbf{r}$).
Aug
17
comment Evaluating Elliptic Integrals in terms of Gamma Function
Did you read this?
Aug
2
comment What is the area covered by a Random walk in a 2D grid?
I like the third question...
Aug
2
comment What is the area covered by a Random walk in a 2D grid?
I'm not sure this is a question where one is expected to give an "exact" answer. It looks rather like a test where one tries to test ones intuition and ability to obtain rough estimates quickly. But if you are given an unlimited amount of time, the easiest is to quickly program it on a computer...
Jul
8
comment Asymptotics in differential equations
The answer to these questions are quite involved and I am not sure it can be reasonable answered in the context of this forum. I can only point you to the book "Advanced mathematical methods for scientists and engineers" by Bender and Orszag where the questions are answered (part of it in Sec 3.7, Ex 3).
Jul
7
comment Series expansion of reciprocal function of Generalized Exponential Integral
Around which point? In any case, you might be interested to look at the Lagrange inversion theorem.
Jul
7
comment Heat equation with fourier transformation
Insert the expression $u(x,t) = \int\!dk\,e^{i k\cdot x} \hat u(k,t)$ into your differential equation.
Jun
27
comment A certain Complex line integral
I would trust your book in this case. Can you show what you have done? (be careful about the multi-valuedness of the logarithm function!)
Jun
24
comment How can I solve the integral below using complex variables?
Hint: $\sin x= \mathop{\rm Im} e^{ix}$...
Jun
14
comment Timesing by a negative switches the limits on an integral?
You know that $\int_a^b f(x) dx = F(b)- F(a)$. I guess you can take it from here...
Jun
8
comment How can I solve $\int \sqrt{x}^\sqrt{x}dx$
I doub't that Rellek's answer is correct (never trust CAS blindly)...
May
28
comment Prove that there is a real number $a$ such that $\frac{1}{3} \leq \{ a^n \} \leq \frac{2}{3}$ for all $n=1,2,3,…$
Implementing the algorithm on a computer leads to the result $\alpha \approx 5.62144865272$.
May
21
comment Integrate with $-d(x/y)$
What I am trying to say is that the line-integral does not depend on the path but only on the end-points. In fact it only depends on the ratio $y/x$ of the starting point and the end point.
May
21
comment Integrate with $-d(x/y)$
One question: wouldn't all these approaches in the end lead to the same result?
May
14
comment Circular solution of Kepler Problem
I'm sure this question is not self-contained. What is the Kepler problem? What is $a$ and $q$ and $t$?
May
14
comment How to do integration by parts with brownian motion?
Hint: Integration by parts originates from the product rule for derivates. Do you know how to determine $d( f_t g_t)$ for two stochastic processes $f_t$ and $g_t$?
May
14
comment How to do integration by parts with brownian motion?
Why do you know you want to perform integration by parts?
May
7
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