Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
5
votes
3answers
151 views
Integration gives ComplexInfinity when it shouldn't
A simple example of my problem is that
Assuming[k ∈ Reals, Integrate[Exp[l]/((1 + Exp[l])*Exp[k*l]), l]] /. {k -> 2}
gives ...
4
votes
0answers
110 views
Version 8.0 integrates but Version 9.0.1 doesn't
I am trying to run the following integral in version 9.0, but it fails:
...
15
votes
2answers
213 views
Inconsistent results from equivalent integrals
Why is Mathematica returning different values for these two integrals:
I am just being introduced to complex integration, so it's possible that I have a misunderstanding of how this works, but in ...
8
votes
4answers
437 views
Plot a 2D vector path onto a surface
In my calculus 3 course, we're studying gradients and have a project that takes a combination of 3D Gaussian radial surfaces and a basic parametric path $r(t) = \{x(t),y(t)\}$ to see how the gradient ...
4
votes
4answers
204 views
Differentiating space curves
I'm trying to do some very basic differential geometry of space curves. For example, a space curve $\gamma:\mathbb R\to\mathbb R^3$ has unit tangent and normal vectors given by
...
3
votes
1answer
89 views
Why is the output of my limit expression an interval?
Why is the output of the limit below an interval? It should be precisely $1$.
...
1
vote
0answers
58 views
Symbolic Integration of Boole [closed]
Why is
Integrate[Boole[x < 1], q]
resulting in
Piecewise[{{x, x <= 1}}, 1]
I'd expect
...
5
votes
1answer
106 views
Definite Integral over a path
What does
Integrate[f[z], {z, a, b, c, d}]
exactly calculate? Is it
$$\int_a^b f(z)\, \mathrm{d}z +\int_b^c f(z)\, \mathrm{d}z
+\int_{c}^d f(z)\, \mathrm{d}z ...
0
votes
1answer
85 views
Integrate function without specifying limits of integration
I've been having trouble to make mathematica evaluate an integral without specifying the values of the limits of integration. I mean, if I write
...
1
vote
1answer
171 views
0
votes
1answer
200 views
No output for N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]
Is my input below correct? I've received no response from Mathematica.
N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]
Thank ...
1
vote
2answers
248 views
3N-dimensional integral
I'm trying to compute a multidimensional integral with a variable number of dimensions.
The integral is as follows:
$$
\int d^{3N}\!p~e^{-\frac{\beta}{2m}\vec p^2}.
$$
I have tried this
...
-5
votes
1answer
90 views
Help in coding of differential equations [closed]
I need some help with Mathematica. How can I do the following?
Starting with f = y[0]^2 (y[0] is basically y with 0 subscript) ...
0
votes
1answer
782 views
Quick Hessian matrix and gradient calculation?
I am absolutely new to Mathematica and I actually want to try implementing a little optimization method .
Long story short assuming I have a predefined two-variable function f(x,y) I want to ...
6
votes
0answers
110 views
Is there a way to teach integrate new solutions?
I have an integral which I can solve, but integrate cannot:
...
0
votes
2answers
202 views
Integrating hat functions
I am trying to integrate a hat function for a project that I am doing and have found a method to do so but I find it sloppy. Currently I have the basis function
...
2
votes
3answers
239 views
Symbolic derivative of $n$-term product
I want to determine the relationship that must exist between the $x_i$ and $y_i$ such that
$$
\frac{\partial}{\partial\theta} \prod_{i=1}^n \frac{f(x_i,\theta)}{f(y_i,\theta)} = 0,
$$
where
$$
...
4
votes
1answer
148 views
Integration over region given by inequality [duplicate]
Sometimes we need to integrate over some bounded region given by inequality/inequalities. Consider the following simplest example of area of an ellipse (LaTeX code):
$\int_S dx dy$, where $S = \{ ...
0
votes
0answers
177 views
Mathematica does not evaluate my integral. Am I doing something wrong? [closed]
When given the following integral,
Integrate[HurwitzZeta[Log[2, u], q], u]
Mathematica returns it unevaluated. The answer should be
HurwitzZeta[Log[2, u], ...
1
vote
0answers
105 views
A curious double zeta evaluation [closed]
While investigating the evaluation of a double Euler sum (a.k.a. a double zeta function),
$$\zeta(r,s)=\sum_{j=1}^\infty \sum_{k=1}^{j-1}\frac1{j^s k^r}$$
in Mathematica, I chanced upon most ...
-1
votes
1answer
99 views
Solving an equation for asymptotic dependence of the solution on a coefficient
I have an equation I want to solve, so I entered the following into Mathematica.
(x^(17/6))/(a^(17/6)) - (x^2)/a -1 == 0
where I assume $a>>1$ and $x$ is ...
1
vote
1answer
99 views
How can I calculate a limit with a free variable?
For example, when I evaluate
Limit[(1 + x^n + (x^2/2)^n)^(1/n), n -> Infinity]
Mathematica does not output any result. When I evaluate
...
3
votes
1answer
189 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
...
0
votes
0answers
91 views
Strange result from integrate
I am working on the following problem. However, the first task takes too long, although the answer 0 is correct. In the second task, to reduce the calculation time, ...
2
votes
1answer
121 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 ...
0
votes
1answer
394 views
Given x[u,v], y[u,v], and f[x,y] how do I find D[f,x] in terms of u,v?
I have two functions x = x(u,v) and y = y(u,v). The chain rule says that for a function f(x,y), df/dx = df/du du/dx + df/dv dv/dx, and similarly df/dy = df/du du/dy + df/dv dv/dy.
How do I get ...
7
votes
3answers
900 views
Finding unit tangent, normal, and binormal vectors for a given r(t)
For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$.
I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...
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!
...
3
votes
3answers
406 views
Definite integral takes a very long time
I'm trying to integrate the following function:
$$
r_e=\int_0^z\frac{dz}{\sqrt{\Omega_m(1+z)^3+\Omega_\Lambda}}
$$
where $\Omega_\Lambda=1-\Omega_M$ and both $\Omega_\Lambda$ and $\Omega_M$ are real ...
2
votes
2answers
165 views
integral, explicit form
I want to estimate the ratio of integrals:
$$
\frac{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_1 \left(\frac{4}{T^3}+1\right)}}{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_0 ...
3
votes
1answer
93 views
Why does Assuming for Integrate not work as expected?
I'm trying to perform the following integral with Mathematica 7:
...
2
votes
0answers
107 views
About calculating Integrals
I am trying to Integrate the following Integral (all of the variables are reals)
$$\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 ...
20
votes
4answers
553 views
An apparently “simple” limit?
Let $c$ and $h$ be real values.
I was using Mathematica to compute the limit $(h \rightarrow \infty)$ of the following expression:
$$
\frac{\left(h^2 +c^2 h^2 + \sqrt{4 h^2+\left(h^2+c^2 ...
2
votes
0answers
95 views
A triple sum related question
I'm trying to compute the triple sum
Sum[1/(i! j! k! ), {i, 1, Infinity}, {j, i + 1, Infinity}, {k, j + 1, Infinity}]
but Mathematica doesn't return
any value. ...
1
vote
0answers
45 views
Interested in knowing what substitutions were made to perform an Integrate[]? [duplicate]
Possible Duplicate:
How does Mathematica integrate?
Mathematica can perform the following integral with apparent ease (returning very fast with the result)
...
2
votes
1answer
104 views
Computing derivatives of a moment generating function
Dear Mathematica users,
I'm trying to compute higher order derivatives of a moment generating function and then evalutate them in 0 (in order to get some moment conditions for a GMM estimation).
...
0
votes
1answer
122 views
Different expressions for an integral if I split the region of integration
Consider the assumptions
...
1
vote
0answers
123 views
Help for double parametrized integration: algebraic vs Mathematica solutions
I have to solve a double integral with parametrized functions, that is (written as a latex equation)
$$
\int_{-\infty}^\infty \int_0^\infty u(t)u(t-\Delta)\frac{1+e^{-2\int_{t-\tau-\Delta}^{t-\tau} ...
6
votes
1answer
348 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, ...
0
votes
1answer
145 views
Evaluate multivariable function [closed]
I'm trying to use Mathematica to evaluate many values of $f(x,y) $, like $f(-\pi,\pi) $ for
$$f(x,y) = \left( \frac{-1}{4}\sin \left( \frac{x-y}{2} \right)\sin y \right)\left( \frac{-5}{4}\sin ...
1
vote
1answer
176 views
2
votes
2answers
192 views
Order of integration changes output of indefinite multiple integral in Mathematica 7
I'm trying to integrate a form-factor used in the calculation of radiation between two rectangles in perpendicular planes. While the integral is usually done over fixed limits, I am trying to do the ...
3
votes
1answer
184 views
Turn list of edges into a polygon function
I have a list of coordinates that define the edges of a polygon and I would like to get a function defining the area Inside out if it (The polygon is convex and the points are in order)
So that for ...
8
votes
5answers
1k views
Finding the centroid of the area between two curves
When I have an area bounded by curves, is there a built-in way to find the center of the area? Or do I have to plot it first and then use ComponentMeasurements on ...
0
votes
0answers
160 views
How can I calculate an integral, perhaps using residues?
Could you advise me on how to calculate the following integral, perhaps by using Residue?
...
2
votes
4answers
176 views
How to evaluate this indefinite integrate $\csc(4x)\sin(x)$
I tried to integrate the following integral using Integrate[Sin[x]Csc[4x],x] and I am getting a strange result.
$$\frac{1}{8 \sqrt{2}}\left(-2 i ...
5
votes
4answers
522 views
How to find the sum all even numbers of this sequence?
I have a sequence $(u_{n})$
$$u_1= 1, \quad u_2 = 2, \quad u_3 = 3, \quad u_{n}= -u_{n-3} + 3u _{n-2} +2 u_{n-1}, \quad \forall n \geqslant 4.$$
I want to list the first $20$ terms of this sequence ...
6
votes
3answers
212 views
How to calculate this sum?
I want to find the sum
$$S=f\left(\dfrac{1}{2012} \right) +f\left(\dfrac{2}{2012} \right) +\cdots + f\left(\dfrac{2011}{2012} \right), $$
where $$f(x) = \dfrac{4^x}{4^x + 2}.$$
I tried
...
0
votes
1answer
72 views
Why does “Pattern(1,0)[w,_]” show up in the resulting expression of a differentiation? [closed]
I would like to differentiate the function s, and be able to evaluate it for different w afterwards. I tried the following:
...
1
vote
3answers
248 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 ...
