Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
3
votes
1answer
92 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.
...
3
votes
2answers
144 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 ...
3
votes
1answer
331 views
Symbolic integration in the complex plane
Context
While answering this question, I defined (symbolic and numerical) path integrations as follows
...
3
votes
1answer
165 views
One Integral — Two Results
I compared Mathematica's default integral evaluation to what you get by computing the indefinite integral and then plugging in the limits.
(I did this because the latter approach was much faster for ...
3
votes
2answers
215 views
3
votes
2answers
565 views
How to substitute numeric values in a symbolic Jacobian matrix?
I have a multi-variate function from $\mathbb{R}^n\to\mathbb{R}^n$. Choosing any desired initial vector, we can produce the corresponding function value, which is a vector as follows. The main problem ...
3
votes
1answer
264 views
Computation of parametric integral
I am trying to compute the integral
Integrate[(g^(u^(g - 1)))/(1 + u^g), {u, 0, t}]
but as an answer I get my input expression. There must be something wrong ...
3
votes
1answer
92 views
Why does Assuming for Integrate not work as expected?
I'm trying to perform the following integral with Mathematica 7:
...
3
votes
1answer
184 views
Turn list of edges into a polygon function
I have a list of coordinates that define the edges of a polygon and I would like to get a function defining the area Inside out if it (The polygon is convex and the points are in order)
So that for ...
3
votes
1answer
188 views
Integrating over Bessel Function erroreous? (Hankel Transform)
The Hankel Transform is given by
Integrate[f[x] x BesselJ[0,x t],{x,0,Infinity}]
It is self-inverse, so
...
2
votes
3answers
237 views
Symbolic derivative of $n$-term product
I want to determine the relationship that must exist between the $x_i$ and $y_i$ such that
$$
\frac{\partial}{\partial\theta} \prod_{i=1}^n \frac{f(x_i,\theta)}{f(y_i,\theta)} = 0,
$$
where
$$
...
2
votes
4answers
176 views
How to evaluate this indefinite integrate $\csc(4x)\sin(x)$
I tried to integrate the following integral using Integrate[Sin[x]Csc[4x],x] and I am getting a strange result.
$$\frac{1}{8 \sqrt{2}}\left(-2 i ...
2
votes
2answers
176 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 ...
2
votes
3answers
594 views
How can I differentiate Numerically?
Mathematica has two ways to integrate: Integrate and NIntegrate.
But what about D? ...
2
votes
1answer
340 views
Speeding up a slow indefinite integral
I have found an alternative way to express an old solution:
...
2
votes
3answers
121 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?
...
2
votes
2answers
164 views
integral, explicit form
I want to estimate the ratio of integrals:
$$
\frac{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_1 \left(\frac{4}{T^3}+1\right)}}{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_0 ...
2
votes
1answer
240 views
How to find all roots and maxima and minima and graph them
I need to find all the roots of this function.
I know it is simple to find by hand, however, I wish to learn how to do it so I can apply it later. The problem is that it only gives me one root.
...
2
votes
1answer
144 views
Checking if first derivative is zero at a given point
I have a function
V[a_, h_, tau_] := (Sqrt[3]/2) h (Sqrt[3] a + h/3 tau)^2
now I want to check, whether its first derivative is zero in a given point. Say for ...
2
votes
2answers
146 views
integrating slightly complicated expression which includes Abs
I have been waiting for Mathematica to give me something for the following integral, errors welcome, but it has been "running" for almost 30 minutes now.
...
2
votes
1answer
356 views
Lie-Bracket of two vector fields
I'm new to Mathematica (installed couple of hours ago) and I need to compute a few Lie brackets between two vector fields $f$ and $g$.
$$ f\left(\mathbf{x}\right) =
\left(
\begin{array}{c}
...
2
votes
1answer
103 views
Assumptions with D
I want to give assumptions for the D function. Say I want to calculate $\frac{d|x|}{dx}$ for $x>0$, which is 1.
I write ...
2
votes
3answers
126 views
Multiple assumptions in integral
I want to add two assumptions, so I can get this probability density function to equal 1, though I can't get a solution.
...
2
votes
1answer
129 views
Integrate[(1 + x/n)^n*Exp[-x], {x, 0, Infinity}]
I evaluated
Integrate[(1 + x/n)^n*Exp[-x], {x, 0, Infinity}] .
thinking the answer should be approximately $\sqrt{\pi n/2}$. Mathematica gave me
...
2
votes
2answers
192 views
Order of integration changes output of indefinite multiple integral in Mathematica 7
I'm trying to integrate a form-factor used in the calculation of radiation between two rectangles in perpendicular planes. While the integral is usually done over fixed limits, I am trying to do the ...
2
votes
1answer
119 views
How can I handle curve singularity in this NIntegrate integration?
Yesterday I asked a question about the non converging integral. Woods told me that it is due to the function which has a singularity along a line which passes through the integration region.
(Why ...
2
votes
1answer
104 views
Computing derivatives of a moment generating function
Dear Mathematica users,
I'm trying to compute higher order derivatives of a moment generating function and then evalutate them in 0 (in order to get some moment conditions for a GMM estimation).
...
2
votes
1answer
255 views
Finding residues of multi-dimensional complex functions
Say I have a function $f$ of $n$ complex variables, $\{ z_i \}_{i=1}^{i=Nc}$. And then I want to contour integrate the expression such that for each $z_i$ its an integration on an unit circle about ...
2
votes
1answer
185 views
Integral not simplifying
I specify a function in terms of an integral and then try to evaluate it with Simplify. However, the answer is not really simplified to what it should be.
...
2
votes
1answer
161 views
About high dimensional integrals
I want to be able to do high dimensional integrals like,
(..naively I wrote it as this..)
...
2
votes
0answers
77 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:
...
2
votes
0answers
89 views
Derivatives of list elements
Could someone explain the odd behavior of the Derivative function when drawing arguments from lists? We have,
...
2
votes
1answer
124 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. ...
2
votes
1answer
156 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:
...
2
votes
0answers
106 views
About calculating Integrals
I am trying to Integrate the following Integral (all of the variables are reals)
$$\int Exp(-(\cos^{-1}\left[\frac{\text{n}_0 (\text{v}_0-\text{x}_0)+\text{n}_1 (\text{v}_1-\text{x}_1)+\text{n}_2 (u ...
2
votes
0answers
92 views
A triple sum related question
I'm trying to compute the triple sum
Sum[1/(i! j! k! ), {i, 1, Infinity}, {j, i + 1, Infinity}, {k, j + 1, Infinity}]
but Mathematica doesn't return
any value. ...
2
votes
0answers
66 views
How to expand terms within an integral? [duplicate]
Possible Duplicate:
Why aren’t these additions of integrals and summations equal?
I am trying to expand all the terms in a sum in order to apply assignment rules later, but can't figure out ...
2
votes
0answers
163 views
Numerical-Symbolical Integration (Calculus)
I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals.
The problem with my function is ...
2
votes
0answers
147 views
How to plot function & integral with vector variable?
I want to plot functions & integrals with vector variable the present in this paper.
For example the equation (5) at p. 3: I want to plot a chart like figure 5, i.e. the $x$-axis is the angle ...
2
votes
0answers
284 views
Simple contour integral with a parameter gone wrong
I run into the following problem, I tried to evaluate a very simple integral:
Assuming[ a > 0 , Integrate[Sin[a*s]/(s - I)^2, {s, -Infinity, Infinity}]]
...
1
vote
3answers
244 views
How do I evaluate several n-th derivatives of a function at one point?
I have a question where I have to compute a Table containing $f^{(n)}(0)$ for n = 1, ..., 5, where $f^{(n)}$ denotes the $n$th ...
1
vote
2answers
247 views
3N-dimensional integral
I'm trying to compute a multidimensional integral with a variable number of dimensions.
The integral is as follows:
$$
\int d^{3N}\!p~e^{-\frac{\beta}{2m}\vec p^2}.
$$
I have tried this
...
1
vote
2answers
142 views
Write a function that returns the logarithmic derivative
How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
1
vote
2answers
137 views
Solve f'[x]==0 for x
I tried the following:
f[x_] := x^n/(k + x^(2 n));
Solve[f'[x] == 0, x]
But I got the following response:
Solve::nsmet: This system cannot be solved with the ...
1
vote
1answer
67 views
Integration of a rational function
I am trying to solve the following rational integral (I got assistance here):
$$\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 ...
1
vote
1answer
101 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 ...
1
vote
2answers
180 views
Quickly differentiate and evaluate a function of several variables
How can I differentiate a function with respect to several variables and evaluate it at the same time ? I want to specify also the variable index that I want to differentiate and the number of times I ...
1
vote
1answer
101 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
156 views
Calculus 1 Related Rates -Total Derivative issues
I'm trying to do part a) of this calculus 1 problem in Mathematica V9:
http://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx#Deriv_Rates_Ex4
Warning noob code below!
...
1
vote
2answers
263 views
How to draw a tangent to a surface in a given direction?
It seems quite embarrassing for me, but somehow I can't draw a tangent line to a surface in a given direction. Assume that I want to visualize directional derivative of the function, say, ...
