Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
1
vote
2answers
573 views
Find the dimensions of a cylindrical can that will minimize the cost of the material
A cylindrical can is to be made to hold 1 L of oil. Find the dimensions
that will minimize the cost of the metal to manufacture the can.
This is a standard calculus problem.
The volume of the ...
1
vote
1answer
170 views
1
vote
2answers
112 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
1answer
112 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 ...
1
vote
1answer
176 views
1
vote
2answers
73 views
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 ...
1
vote
1answer
96 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
...
1
vote
1answer
169 views
Need help evaluating definite integral to a function of Y
Suppose
$Y = \sqrt{2T}\cos(U)$, $ 0 \le u \le \pi $, and $ 0 \le \cos^{-1}(\frac{y}{\sqrt {2t}}) \le \pi ) $, so $ -1 \le \frac{y}{\sqrt{2t}} \le 1 $, with all $ \mathbb{R}$. The iterated integral ...
1
vote
1answer
138 views
How to collect q[t] from the following integration
As shown in the following program, the q[t] in a can be collected from the integration by defining the integration of ...
1
vote
1answer
103 views
How to explain the results of the following integrals?
Why does the following program lead to different results of a21 and a211?
...
1
vote
1answer
98 views
Simplifying an Integral over Two DiracDeltas
Integrate[DiracDelta[a + k] DiracDelta[-b + k], {k, -\[Infinity], \[Infinity]}]
(*DiracDelta[a + b]*)
This works fine.
But
...
1
vote
1answer
430 views
How to solve this integral
I'm trying to deal with this article, but I don't understand how equations 5.9 and 5.10 were obtained. I tried to use Mathematica 8 to solve it, but the answer was different.
I have a problem with ...
1
vote
0answers
69 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 ...
1
vote
0answers
118 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 ...
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
...
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
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)
...
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} ...
1
vote
0answers
151 views
Function approaching incorrect limit in mathematica [closed]
I am interested in the complex function
$f(z)=\frac{1}{a}\log\left[2\sinh(a\sqrt{z})\right]$.
where $a > 0$ is a real parameter. Clearly for large $a$ this approaches $f(z) \to \sqrt{z}$.
But ...
1
vote
0answers
255 views
Calculating the mean curvature of a surface - suggestions
I am attempting to calculate the mean curvature [1, 2] of a surface defined by a function of x and y.
My function is rather ...
1
vote
0answers
197 views
About doing an integral
For a given integer $N$ and some function $f(x,y)$ I want to be able to do an integration of the kind,
$\int_{0} ^{\infty} \prod_ {i=1}^N da_i e^{[\sum_{n=1}^{\infty} \frac{1}{n} \left[ N + ...
1
vote
0answers
133 views
Asymptotic Rate of Growth
How can I calculate the Asymptotic Rate of growth of a function, for instance like:
$X^3 - X^2 - X -1$
EDIT:
For instance, as you can see in this graph, after the 1200 the function approximates to ...
1
vote
0answers
116 views
How to move differentation before the integral?
I have quite a lot expressions that need to be integrated after switching the integral sign with differentation operator. The additional problem is that the bounds are dependent to one of the ...
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 $dx/dt = 2$ ...
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
...
0
votes
2answers
318 views
Integral with the derivative of Dirac delta does not evaluate correctly?
Integrate[DiracDelta'[y - z] DiracDelta[x - z], {z, -Infinity, Infinity},
Assumptions -> x \[Element] Reals && x \[Element] Reals]
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 ...
0
votes
1answer
197 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 ...
0
votes
1answer
193 views
How to define a derivative/Variation operation in Mathematica from scratch
I am looking for a method in Mathematica 8 to define my own derivative/variation (independent of built-in operations). I do not want to re-define built-in objects since I fear that this could cause ...
0
votes
1answer
71 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 ...
0
votes
2answers
195 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:
$$\int\frac{d^d ...
0
votes
1answer
83 views
NumericQ prevents evaluation at a numerical value sometimes
I set up a symbolic integral, to be evaluated only when some of the symbols have been replaced by numbers. The evaluation after assigning numbers to the symbols is still symbolic for some reason. The ...
0
votes
1answer
85 views
Integrate function without specifying limits of integration
I've been having trouble to make mathematica evaluate an integral without specifying the values of the limits of integration. I mean, if I write
...
0
votes
1answer
775 views
Quick Hessian matrix and gradient calculation?
I am absolutely new to Mathematica and I actually want to try implementing a little optimization method .
Long story short assuming I have a predefined two-variable function f(x,y) I want to ...
0
votes
1answer
145 views
Evaluate multivariable function [closed]
I'm trying to use Mathematica to evaluate many values of $f(x,y) $, like $f(-\pi,\pi) $ for
$$f(x,y) = \left( \frac{-1}{4}\sin \left( \frac{x-y}{2} \right)\sin y \right)\left( \frac{-5}{4}\sin ...
0
votes
1answer
71 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
125 views
0
votes
1answer
392 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 ...
0
votes
1answer
122 views
Different expressions for an integral if I split the region of integration
Consider the assumptions
...
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:
...
0
votes
2answers
267 views
Why Can't Mathematica Integrate this?
I have the following problem from a textbook I am trying to integrate:
So, following the directions in text, I am required to integrate each function. However, I cannot get Mathematica to integrate ...
0
votes
1answer
53 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 ...
0
votes
0answers
30 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:
...
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:
...
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
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 ...
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], ...
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, ...
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?
...
