Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
1
vote
0answers
76 views
Multi-dimensional integral in the complex plane with poles and essential singularity
I've passed the last week searching a way to numerically integrate this multi-dimensional integral in the complex plane at the poles and avoiding the singularity at z=0:
$$
\oint_{C}\oint_{C\ auound\ ...
0
votes
0answers
4 views
Differential equation change of variables [migrated]
I have differential equation, $xy''(x) +(n+1-x)y'(x) + ay'(x)=0$
If I let $x=r^t$ then how to plug in this and how to use change of variable to get the differential equation for r, instead of x?
...
0
votes
0answers
115 views
Why wolframalpha.com can be more powerful than Mathematica sometimes? [closed]
I wanted to determine whether the infinite series of $u_n=(\sqrt{n+1}-\sqrt{n})^{\frac{1}{2}}\ln{\frac{n-1}{n+1}}$ converges.
...
0
votes
0answers
63 views
Non-Solvable PDE?
I would like to know whether this PDE is solvable and if yes, for which values of $a$.
...
0
votes
0answers
51 views
recurrence relations
If I write
f[i_] := Expand[FunctionExpand[x^(i/5) LerchPhi[x, 1, i/5]]]
for any i < 5, the result is a linear combination ...
4
votes
1answer
140 views
Mathematica 9 can't integrate this function but earlier versions could
Integrate[ ArcTan[x]/(1 + x) Log[(1 + x^2)/2], {x, -1, 1}]
I used Mathematica 9.0.1 on Windows7 32bit, Mathematica 9 cannot compute this, but Mathematica 8 gives ...
3
votes
2answers
174 views
Create polygon using edge lengths and area
Four-sided convex land plots are usually denoted with edge lengths and area.
How do I create a Polygon Object with these parameters in Mathematica ?
0
votes
0answers
46 views
Interpretation of output derivative expression [duplicate]
I am trying to write Mathematica file to find Div, Grad, Laplacian, etc. in coordinates ...
1
vote
1answer
78 views
finding poles of a function
Is there a command to find the poles of a function $f=f(z)$?
example: let $$f(z) = \frac{1}{z^2-1}$$ then we know that the poles are at
$z=\pm 1$ but is there a special command in mathematica to do ...
1
vote
1answer
57 views
Double Integral and Assumptions
I'm afraid this is going to be a really stupid question.
Evaluating the following definite integral
Integrate[Sqrt[1 - (x^2 + y^2)], {x, -1, 1}, {y, -1, 1}]
...
1
vote
2answers
143 views
Finding normals to a curve through a given point
I want to find x on curve $y(x)$, where curve $y(x)$ is perpendicular to point $(x_0,y_0)$.
for this I minimize the distance between points $(x,y(x))$ and $(x_0,y_0)$, here's an example for point ...
2
votes
1answer
177 views
Laurent series expansion
Can someone share how to find a Laurent series expansion of
$$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$
centered at zero on the annular disk $1<|z|<2$?
5
votes
1answer
82 views
Numerical contour integrations in the complex plane - contour deformation gives different answer for analytic kernel
I am trying to do a contour integration in Mathematica numerically. In particular, I'm checking the identity:
$$ H_m^{(1)}(z) =\frac{i^{-m}}{\pi}\int_{-\pi/2 + i \infty}^{\pi/2 - i \infty} \exp[i m ...
2
votes
0answers
47 views
3
votes
1answer
196 views
n-fold symbolic integral in Mathematica
I am trying to compute symbolically a n-fold integral (n is a parameter of a function) over, say, the cube [0,a]^n. My code looks like this
...
0
votes
1answer
105 views
Can I take derivative of a function that represents a piece of music?
Can I take the derivative of a function that represents a piece of music? The music is given in .mp3, .midi or whatever comes in handy.
9
votes
2answers
281 views
Numerical partial derivative
For a one-variable numerical function, it's simple to calculate the derivative at a point with Derivative as Szabolcs has pointed out before:
...
-1
votes
0answers
65 views
Why is this calculation too slow?
I want to compute the first and second derivatives of a relatively simple function but Mathematica is either taking ages to compute them or aborts printing the following message:
"Simplify::time: ...
0
votes
1answer
246 views
No output for N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]
Is my input below correct? I've received no response from Mathematica.
N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]
Thank ...
2
votes
0answers
43 views
Verifying integration by parts of an arbitrary function [duplicate]
Suppose that I have an arbitrary differentiable function $G$ which depends on $s$: $G(s)$.
Now suppose that I want to do the following integral: $$\int ds \;\; s \frac{\partial G(s)}{\partial s}.$$
...
9
votes
5answers
2k views
Finding the centroid of the area between two curves
When I have an area bounded by curves, is there a built-in way to find the center of the area? Or do I have to plot it first and then use ComponentMeasurements on ...
1
vote
1answer
83 views
Derivative inside a function
I am trying a problem that should be simple: to create a function that contains a derivative. I need to do a more complex example, but even with the simplest I'm having trouble:
Let's consider
...
0
votes
2answers
413 views
About generating power series
For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows,
...
1
vote
0answers
67 views
Cauchy principal value integral of a list of numbers. How?
I have a list of numbers that are numerical samples of a function for which I need to find the Cauchy principal value integral. I thought I should be able to combine Interpolation with Integrate to do ...
3
votes
1answer
180 views
Is it possible to impose “Assumptions” in DSolve or equivalent? (differential equation solving)
When DSolve tries to solve differential equations, it is sometimes not smart enough to generate conditions according to different possible value of parameters. ...
5
votes
1answer
98 views
Is it possible to find a limit of a sequence given by its recurrence relation?
I need to calculate a limit of a sequence given by its recurrence relation. I tried the following:
...
5
votes
3answers
495 views
recursive integration
I am trying to do multiple integrations recursively. For instance, I would like to do the following equation for arbitrary integer $n$:
$\displaystyle R_n(t) = \int_0^t \mathrm dt' R_0(t-t') ...
2
votes
1answer
180 views
Volterra integral equation : 'literally match the independent variables' message
I want to solve an Volterra type Integral equation,
and as a practice I entered the following code to my mathematica:
...
11
votes
2answers
209 views
What kind of hypergeometric function is it?
I found a formula for an integral of a product of three Bessel functions at The Wolfram Functions Site:
I cannot understand what kind of hypergeometric function it is.
The Mathematica code given ...
2
votes
3answers
128 views
Manipulate fails with f[x]=x^k/(1+x^k)
I have:
Clear[f]
f = Function[x, x^k/(1 + x^k)];
Manipulate[
Plot[f[x], {x, 0, 5}],
{k, 1, 10}]
But nothing draws as I move the slider. Am I missing something?
...
3
votes
1answer
114 views
Evaluating double Integral
While trying to evaluate the integral $\int_{y=0}^{x_2}\int_{x=0}^{min(x_1,y)} n (n - 1) (1 - y)^{(n - 2)}dxdy $ , Mathematica does not seem to yield any results.
...
5
votes
4answers
194 views
How do I obtain the correct double limit?
The command
Limit[(Sin[x^2] + Sin[y^2])/ (x - y) /. x -> 0, y -> 0]
(*
0
*)
I think that Mathematica finds the iterated limit instead of the double ...
14
votes
4answers
588 views
Finding Limits in several variables
Is there a way to find a limit of a multivariable function, like
$$\lim_{(x,y)\to (0,0)} f(x,y)$$
with Mathematica?
When $f$ is continuous, we can use
$$\lim_{(x,y)\to (0,0)} ...
6
votes
1answer
379 views
How to expand a function into a power series with negative powers?
Is there any way to expand this expression
a+b(1-Exp[-T/(b c)]/(z-Exp[-T/ (b c)])
(where a, ...
1
vote
2answers
159 views
Write a function that returns the logarithmic derivative
How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
3
votes
1answer
395 views
Definite and Indefinite integral give different results for piecewise function
I have the following function:
$$
f(q,y)=
\begin{cases}
\tfrac{11720+p}{37791360} & -11720<p<-7720 \\
0 & \text{True}
\end{cases}
$$
where $p = 443\ y-777600\ \sin^{-1}\left(\frac{q ...
1
vote
1answer
73 views
Integration of a rational function
I am trying to solve the following rational integral (I got assistance here):
$$\int_{-\infty}^{\infty}{\frac{a+x}{b^2 + (a+x)^2}\frac{1}{1+c(a-x)^2}}dx$$
where $\{a, b, c\}\in \mathbb{R}$. I would ...
2
votes
0answers
84 views
Is this result wrong because of calculation time? (and more questions about Assumptions)
I am confused with the Integrate Given by Mathematica. First let's see a one-dimensional case:
...
0
votes
1answer
86 views
Integrate of Heaviside Function returns an error answer
I try to evaluate an Integral of a Heaviside function, but it turns out with an erroneous output(zero). Here is my integral:
...
0
votes
1answer
76 views
Taking derivative of Euler relation [closed]
I have defined the following function, which is the Euler relation for $\cos\,x$.
f[x_] := 1/2*(Exp[I*k*x] + Exp[-I*k*x ] )
I want to take the derivative with ...
6
votes
3answers
1k views
How to find the nth derivative?
This question is not the same as my last one. How do you find the $n$-th derivative where $n$ is a variable?
For example, you can find the nth derivative for a specific $n = 3$
...
9
votes
2answers
296 views
Derivative from the left and right
I am currently trying to write a script that takes a curve $C$, a starting point $p$ and a direction vector $\vec{v}$ and calculates the path of a beam starting at $p$ in direction $\vec{v}$ when it ...
1
vote
3answers
255 views
How do I evaluate several n-th derivatives of a function at one point?
I have a question where I have to compute a Table containing $f^{(n)}(0)$ for n = 1, ..., 5, where $f^{(n)}$ denotes the $n$th ...
9
votes
2answers
223 views
Find closed form expression for series expansion coefficients [duplicate]
Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function?
Series will only give the explicit ...
1
vote
2answers
74 views
7
votes
1answer
91 views
How to calculate this integral? Integrate[BesselJ[0, x - BesselJZero[0, 1]]/x, {x, -Infinity, Infinity}]
I tried to calculate the following integral, but it returned unevaluated.
...
8
votes
1answer
136 views
How do I get a general form for n-th derivative of a function? [duplicate]
I tried the following but it basically returns unevaluated:
...
4
votes
2answers
114 views
Strange behavior of Integrate
I'm trying to calculate the following integral using Mathematica 9.0.1.0
a11=Integrate[Abs[Sin[b+x]],{x,0,2*\[Pi]}]
This should be a simple problem; however, it ...
1
vote
1answer
108 views
how to reduce the time to calculate triple integral
i want to evaluate the following integral, but it takes 15 min to do it. i must reduce the time to calculate it, i have to do a table and create a graph, but takes too long.
anyone have an idea ?
...
1
vote
1answer
104 views
Assumptions are not being applied to integral
I am trying to use assumptions to simplify an integral, but I can't seem to get the assumptions to apply themselves. Here is the code I am using:
Note the expressions in the assumption can be found ...
