Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
21
votes
3answers
1k views
How to find the period of an arbitrary mathematical function?
Is there a function to find the period of an arbitrary (possibly complex) function in Mathematica?
3
votes
2answers
148 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 ...
1
vote
1answer
68 views
How to evaluate an integral
I am trying to evaluate this integral
Integrate[(kx^2/2)*Sin[\[Lambda]x], x]
from -pi/2(lamda) to pi/2(lamda)
Everything there is a constant, and the only ...
3
votes
2answers
135 views
7
votes
0answers
281 views
Dual complex integral over implicit path using contour plot
Context
I am interested in doing double contour integral over paths which are defined implicitely.
For the sake of debugging, let's assume its
$$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
1
vote
1answer
113 views
Sum and NSum gives different solutions
I'm working on a Mathematica lab for Calc. 2, and I ran into a problem last night. I was trying to calculate the midpoint approximation of the definite integral of ...
0
votes
0answers
115 views
Inspecting a function around a singularity [closed]
I am plotting a function which is defined as the ratio between an interpolating function (the solution of some integral equation) and $x^2$, so something like $g(x)=f(x)/x^2$. From the plot of $f(x)$, ...
0
votes
0answers
109 views
Integrating the product of two modified Bessel functions of the second kind [closed]
I want to integrate the product of two modified Bessel functions of the second kind, as follows:
...
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
2answers
138 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 ...
0
votes
2answers
198 views
Using Mathematica to find poles of Gamma functions [closed]
I am concerned about the expression on the RHS of equation A.5 (page 19) in this paper:
$$\int\frac{d^d ...
1
vote
2answers
248 views
3N-dimensional integral
I'm trying to compute a multidimensional integral with a variable number of dimensions.
The integral is as follows:
$$
\int d^{3N}\!p~e^{-\frac{\beta}{2m}\vec p^2}.
$$
I have tried this
...
0
votes
1answer
77 views
Integrating polynomial functions over polytopes with an add-on package
There is a Mathematica package to evaluate integrals over polytopes:
http://library.wolfram.com/infocenter/Books/3652/
In the documentation (Functions.nb file) I ...
2
votes
3answers
127 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.
...
0
votes
1answer
128 views
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 ...
0
votes
0answers
65 views
Complex Integration Optimization
The following code culminates in plots calculated for each value of t as given below.
I have tried compiling one of the functions and adjusting the precision of both the integration and the plotting ...
2
votes
1answer
130 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
...
0
votes
1answer
83 views
NumericQ prevents evaluation at a numerical value sometimes
I set up a symbolic integral, to be evaluated only when some of the symbols have been replaced by numbers. The evaluation after assigning numbers to the symbols is still symbolic for some reason. The ...
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 ...
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:
...
7
votes
2answers
363 views
Simplifying the derivative of $|x|$
Context
In[855]:= D[Abs[x], x] /. x -> 1
Out[855]= Derivative[1][Abs][1]
In[856]:= D[x, x] /. x -> 1
Out[856]= 1
Question
Why is ...
8
votes
4answers
436 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
198 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 ...
-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
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
...
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:
...
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}$$
in Mathematica, I chanced upon most ...
-1
votes
1answer
99 views
Solving an equation for asymptotic dependence of the solution on a coefficient
I have an equation I want to solve, so I entered the following into Mathematica.
(x^(17/6))/(a^(17/6)) - (x^2)/a -1 == 0
where I assume $a>>1$ and $x$ is ...
1
vote
1answer
99 views
How can I calculate a limit with a free variable?
For example, when I evaluate
Limit[(1 + x^n + (x^2/2)^n)^(1/n), n -> Infinity]
Mathematica does not output any result. When I evaluate
...
3
votes
1answer
189 views
Integrating over Bessel Function erroreous? (Hankel Transform)
The Hankel Transform is given by
Integrate[f[x] x BesselJ[0,x t],{x,0,Infinity}]
It is self-inverse, so
...
0
votes
0answers
91 views
Strange result from integrate
I am working on the following problem. However, the first task takes too long, although the answer 0 is correct. In the second task, to reduce the calculation time, ...
2
votes
1answer
121 views
How can I handle curve singularity in this NIntegrate integration?
Yesterday I asked a question about the non converging integral. Woods told me that it is due to the function which has a singularity along a line which passes through the integration region.
(Why ...
0
votes
1answer
393 views
Given x[u,v], y[u,v], and f[x,y] how do I find D[f,x] in terms of u,v?
I have two functions x = x(u,v) and y = y(u,v). The chain rule says that for a function f(x,y), df/dx = df/du du/dx + df/dv dv/dx, and similarly df/dy = df/du du/dy + df/dv dv/dy.
How do I get ...
1
vote
1answer
156 views
Calculus 1 Related Rates -Total Derivative issues
I'm trying to do part a) of this calculus 1 problem in Mathematica V9:
http://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx#Deriv_Rates_Ex4
Warning noob code below!
...
20
votes
4answers
553 views
An apparently “simple” limit?
Let $c$ and $h$ be real values.
I was using Mathematica to compute the limit $(h \rightarrow \infty)$ of the following expression:
$$
\frac{\left(h^2 +c^2 h^2 + \sqrt{4 h^2+\left(h^2+c^2 ...
2
votes
2answers
165 views
integral, explicit form
I want to estimate the ratio of integrals:
$$
\frac{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_1 \left(\frac{4}{T^3}+1\right)}}{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_0 ...
2
votes
0answers
106 views
About calculating Integrals
I am trying to Integrate the following Integral (all of the variables are reals)
$$\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 ...
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
94 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)
...
