Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
0
votes
0answers
16 views
How to substitute functions with numeric values for a model running the variational package?
I have designed and running a model using the variational package. I need to now substitute numeric values and plot the graphs. Can anyone please help or guide with the command input I should be ...
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?
...
1
vote
1answer
103 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:
$$
\oint_{C}\oint_{C\ auound\ ...
0
votes
0answers
117 views
Why wolframalpha.com can be more powerful than Mathematica sometimes? [closed]
I wanted to determine whether the infinite series of $u_n=(\sqrt{n+1}-\sqrt{n})^{\frac{1}{2}}\ln{\frac{n-1}{n+1}}$ converges.
...
0
votes
0answers
63 views
Non-Solvable PDE?
I would like to know whether this PDE is solvable and if yes, for which values of $a$.
...
0
votes
0answers
51 views
recurrence relations
If I write
f[i_] := Expand[FunctionExpand[x^(i/5) LerchPhi[x, 1, i/5]]]
for any i < 5, the result is a linear combination ...
4
votes
1answer
140 views
Mathematica 9 can't integrate this function but earlier versions could
Integrate[ ArcTan[x]/(1 + x) Log[(1 + x^2)/2], {x, -1, 1}]
I used Mathematica 9.0.1 on Windows7 32bit, Mathematica 9 cannot compute this, but Mathematica 8 gives ...
3
votes
2answers
176 views
Create polygon using edge lengths and area
Four-sided convex land plots are usually denoted with edge lengths and area.
How do I create a Polygon Object with these parameters in Mathematica ?
0
votes
0answers
46 views
Interpretation of output derivative expression [duplicate]
I am trying to write Mathematica file to find Div, Grad, Laplacian, etc. in coordinates ...
1
vote
1answer
79 views
finding poles of a function
Is there a command to find the poles of a function $f=f(z)$?
example: let $$f(z) = \frac{1}{z^2-1}$$ then we know that the poles are at
$z=\pm 1$ but is there a special command in mathematica to do ...
1
vote
1answer
57 views
Double Integral and Assumptions
I'm afraid this is going to be a really stupid question.
Evaluating the following definite integral
Integrate[Sqrt[1 - (x^2 + y^2)], {x, -1, 1}, {y, -1, 1}]
...
2
votes
0answers
47 views
1
vote
2answers
144 views
Finding normals to a curve through a given point
I want to find x on curve $y(x)$, where curve $y(x)$ is perpendicular to point $(x_0,y_0)$.
for this I minimize the distance between points $(x,y(x))$ and $(x_0,y_0)$, here's an example for point ...
0
votes
1answer
105 views
Can I take derivative of a function that represents a piece of music?
Can I take the derivative of a function that represents a piece of music? The music is given in .mp3, .midi or whatever comes in handy.
-1
votes
0answers
65 views
Why is this calculation too slow?
I want to compute the first and second derivatives of a relatively simple function but Mathematica is either taking ages to compute them or aborts printing the following message:
"Simplify::time: ...
5
votes
1answer
82 views
Numerical contour integrations in the complex plane - contour deformation gives different answer for analytic kernel
I am trying to do a contour integration in Mathematica numerically. In particular, I'm checking the identity:
$$ H_m^{(1)}(z) =\frac{i^{-m}}{\pi}\int_{-\pi/2 + i \infty}^{\pi/2 - i \infty} \exp[i m ...
2
votes
0answers
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: $$\int ds \;\; s \frac{\partial G(s)}{\partial s}.$$
...
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
...
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 ...
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:
...
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 ...
3
votes
1answer
115 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 ...
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 ...
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 ...
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 ?
...
0
votes
1answer
39 views
Is there a more idiomatic way to solve this implicit differentiation problem?
Here's an exercise from a calculus text by Larson and Edwards:
Find the rate of change of the distance between the origin and a
moving point on the graph of $y = x^2 + 1$ if $dx/dt = 2$ ...
2
votes
0answers
100 views
Derivatives of list elements
Could someone explain the odd behavior of the Derivative function when drawing arguments from lists? We have,
...
0
votes
0answers
31 views
Plot derivative of integral with changing limits [duplicate]
My code is: Plot[D[Integrate[E^(t*(-x^2)),{x,t+2,t^2}],t],{t,-2,3}].
The errors/warnings are:
...
8
votes
0answers
140 views
Why does Mathematica give an incorrect answer to this multiple integral?
This is not a new problem but I would like to understand why Mathematica gives the result that it does. (Volume of a hypersphere)
...
0
votes
1answer
59 views
Simple Question: Derivative of a path
I have a path V[t_]:={3t^2,2,6t}, and I define F[t_]:=V[t]/Norm[V[t]].
I simply want the derivative of ...
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 $1<|z|<2$?
2
votes
2answers
237 views
How do I evaluate a double or triple integral over a region?
Say I need to evaluate the integral $\iiint_W f(x,y,z) dx dy dz$ and $W$ is a region given to me like $W = \{ (x,y,z) : 1 \leq x^2 + y^2 \leq 4, 1 \leq z \leq 5\}$. I don't how to do this with a ...
5
votes
2answers
137 views
Why does Integrate return a solution that is not defined at a particular point when it actually is well defined at that point?
I am trying to compute
Integrate[Sqrt[x^4 + (y - y^2)^2], {x, 0, y}]
Mathematica 8 gives
...
2
votes
2answers
150 views
integrating slightly complicated expression which includes Abs
I have been waiting for Mathematica to give me something for the following integral, errors welcome, but it has been "running" for almost 30 minutes now.
...
5
votes
2answers
114 views
Mathematica cannot calculate a limit
When I evaluate
Limit[E^(-n)*Sum[n^k/(k!),{k,0,n}], n -> ∞]
Mathematica gives me the result
...
1
vote
0answers
75 views
Getting poles of a Gamma functions
Why do the following 2 sequences give different answers?
n = 1.5
Series[Gamma[0.5 - n - x], {x, 0, 2}]
Series[Gamma[-1 - x], {x, 0, 2}]
(..clearly the output from the second expression is ...
4
votes
0answers
118 views
Strange result from evaluating a Limit expression
When I evaluate the limit of (1-Cos[x]) Sin[1/x] at x = 0 in Mathematica 9, I obtained ...
6
votes
2answers
163 views
Why does Integrate declare a convergent integral divergent?
When I try this command
Integrate[1/Sqrt[(s^2 - u)^2 - 1], {s, m, Infinity}, Assumptions -> u > 2 && m > 10]
Mathematica declares that the ...
1
vote
2answers
132 views
Implicit differentiation to find the slope of the tangent line to the graph at the indicated point [duplicate]
I used ContourPlot to plot the graph of x Sin[Pi y] - y Cos[Pi x] == 1 with the following input:
...
1
vote
0answers
119 views
Why won't Mathematica integrate this? [closed]
I have absolutely no programming knowledge but my college requires us to use Mathematica in our calculus classes. This is the first time I've ever had to do any work without a partner and I've gotten ...
-3
votes
1answer
102 views
Limit of a subsequence
I am trying to calculate limit for a subsequence <${ a }_{ {n }^{ 2} }$> because I was trying to see that limits of sequences and subsequences are both same.
I was able to generate the sum for ...
3
votes
2answers
164 views
How do I represent a system dynamics feedback loop?
In System Dynamics, if I want represent the relationship between Speed and Distances, I create a Flow (Speed) and a Stock (Distance) as you can see in this Insight Maker Sample . Heres an Image of how ...
