Questions tagged [calculus-and-analysis]
Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
3,414
questions
0
votes
0answers
10 views
Can't plot derivative of Hankel function [duplicate]
I am trying to plot the first derivative of $H^{(1)}_3 (ix)$ with respect to its argument $ix$, where $H^{(1)}_3 (ix)$ is the Hankel function of the first kind with order $3$, $x \in \mathbb{R}$ is a ...
0
votes
0answers
63 views
Numerical solution of an iterative equation
I am trying to solve the following iterative equation:
where the parameter tao (needed in the previous equation) is defined as:
Here's the parameters and my approach to solving the equation in ...
0
votes
0answers
71 views
Plot of the derivative of a function
I have a function functionSL as a function of t (t<0) where I want to find the extremum ...
0
votes
0answers
57 views
1D Transient Heat Conduction Problem [closed]
I could really use some help with this problem regarding heat conduction through a steel bar
Solve the one-dimensional transient heat conduction problem as follows.
You insert a steel bar that had ...
0
votes
1answer
72 views
Fourier Series of ODE
I am having trouble finding the Fourier series of a 2nd order ODE. Should I be using the piecewise function as well to set up the range for t?
Solve $ y'' + \omega^2 𝑦 = r(t) $, where $ r(t) = |t|, -\...
0
votes
0answers
63 views
zeros or minimum of a multivariable function
what is the most reliable method for finding the zeros or at least the minimum of $f(x,y,z,w,r)= - \frac{3}{96 \pi^{2}z^{4}} \int_{y}^{\infty}\sqrt{x^{2}-y^{2}}x^{2} e^{-x} dx+ \frac{3}{16 \pi^{2}(1-r^...
1
vote
1answer
68 views
Directional derivative of a function of three variables
I'm a Mathematica beginner and I'm and struggling with a problem concerning heat flow, not sure how to set it up with three variables. Any help with what I should input into Mathematica will be much ...
5
votes
0answers
116 views
Incorrect result by DSolve
For real $x$ consider the trivial equation
$$|y'(x)|=-|x|.$$
Since the left side is always positive and the right always negative, there is no solution.
Let's try
...
0
votes
1answer
46 views
Remove complex part of a solution
I have a function intSL[a,zl,zh] where I want to compute its derivative with respect to zl given some values of ...
0
votes
1answer
54 views
Derivative of a set of equations [closed]
I am a new learner of Mathematica, I think this question should be simple, but I just can't get the correct answer...
This is my equations:
p=x+y
q=2x+y
r=p+q
And ...
-1
votes
0answers
36 views
Mathematica outputs sin(Pi*t) as Pi*sin(t) [closed]
Im very new to Mathematica, so spare me if there is a very trivial solution to this.
...
0
votes
1answer
69 views
How to make Mathematica treat y/x as a one variable?
I would like to make for example: $\frac{\partial\frac{2y}{x}}{\partial\frac{y}{x}}$. However, when I put it into Mathematica as D[2y/x,{y/x}] it does not recognize ...
3
votes
3answers
116 views
Plot a set of complex numbers with given argument and absolute value bounds
I want to plot the following complex numbers $$z \in \text{(complex numbers)}:\pi/4 < \arg (z) \leq 5 \pi/4,\ 1 \leq |z| < 2 $$
I don't know how to graph it so that it would look like 2D without ...
-7
votes
0answers
40 views
Integration using the change of variable formula [closed]
I am working on a project for my multivariate calculus class that is focused around using the change of variable formula to manipulate integrals in Mathematica, and I had some questions:
How do you ...
-2
votes
0answers
59 views
How can I analytically solve an integral which has some terms that do not converge in (-∞, +∞)? [closed]
It is to be integrated from -∞ to +∞ and clearly the terms with k1 and k2 don't converge in the interval.
0
votes
2answers
65 views
-3
votes
0answers
81 views
Solve differential equation with integral in Mathematica [closed]
I am reposting this question in hopes I can get some help. In the previous post I didn't put any thing regarding Mathematica So I hope this post is better.
I want to solve the following equation:
...
0
votes
0answers
39 views
SystemException[“MemoryAllocationFailure”] in Integrate
Integrating products and ratios of piecewise linear functions throws the error ...
0
votes
1answer
18 views
Derivative of predictor function
Given some data dat, we would like to generate a predictor function. Therefore we use
...
0
votes
1answer
58 views
Analytical expression for a limit
I have the following equation
$$\Delta v = -g I_\mathrm{SP} \left( 1 + \frac{1}{24} \frac{\mu}{r^3} \frac{g^2 {I_\mathrm{SP}}^2}{T^2} \frac{{m_p}^2}{n^2} \right) ^{-1} \sum _{k=1} ^n \log \left( \...
1
vote
2answers
57 views
0
votes
1answer
44 views
Using Solution to Differential Equation in New Function
I am trying to feed the solutions from my differential equations into another function.
I am using NDSolve to solve two differential equations simultaneously. It ...
-1
votes
0answers
61 views
Solving a certain transcendental equation [closed]
I cannot make Mathematica solve the following transcendental equation using Solve with coefficients a, b, c, d, and ...
0
votes
0answers
75 views
Having trouble making a table of the derivative of a Bessel-function-based expression
Please suggest how I should correct the following code to plot the integral:
...
2
votes
1answer
100 views
Verify a conjectured formula for a modification of a 3D constrained integration successfully solved using Mathematica
I've acquired somewhat indirect--and not fully conclusive--evidence that the solution of a certain three-dimensional constrained integration takes the form
...
2
votes
0answers
52 views
Evaluate fractional derivative
I needed to evaluate the following fractional derivative of $f(t) = e^{t^2}$. The fractional derivative that I'm currently studying is the Grunwald-Letnikov fractional derivative, which is defined as ...
0
votes
1answer
168 views
Elliptical Integration
I have an integral which can be decomposed into three complete elliptical integrals. I want to know the method by which I can achieve this. The integration is the following:
(4 (-1 + y)^2)/(c Sqrt[y (-...
0
votes
0answers
59 views
Derivative of a Definite Integral
I have two equations as follows,
$$a = \int_0^1 dx \frac{c z_s^{d+1} x^d}{\sqrt{(1-(z_s/z_h)^{d+1} x^{d+1})(1-c^2 z_s^{2d} x^{2d})}} \tag{1}\label{1},$$
\begin{align}
S &= \frac{1}{4 z_s^{d-1}}\...
1
vote
1answer
24 views
Calculating boundaries for a multiple integral from inequalities
I was trying to solve for the region enclosed by y=Sqrt[x], z=1+x+y, y=0, and ...
1
vote
2answers
92 views
Triple Integral boundaries and solution
So I'm working on triple integrals, specifically on those where I have a region bounded by various surfaces. (In other words, the ranges for each integrals are not given, but must be calculated.)
I ...
4
votes
2answers
211 views
Hyperbola problem
I'm studying the hyperbola given by the implicit function $x^2/16-y^2/2=1$
I need plot the hyperbola and the asymptotes $y=b/a\,x$ and $y=-b/a\,x$. Then I need to select a point on the hyperbola and ...
1
vote
1answer
62 views
Half-life of a radioactive substance? [closed]
After 4.27 minutes 99.99% of a radioactive substance is present. What is the half-life of the radioactive substance?
What code would I use to solve this problem? I don't know how to start it.
0
votes
1answer
45 views
Issue with Erf function and comparaison with Maple [closed]
I warn you that I am completely new to Mathematica and I apologize in advance if my question is very stupid.
I define the function $f(x)$ in the following way (it is very close to the function ${\rm ...
0
votes
3answers
31 views
I want to maximise my function over a particular domain
I have tried NMaximise. But I am getting an error always. Even if my command is correct. My function is
Cos[π E^x]
and I want to maximise it over the range (-3,3)
4
votes
2answers
240 views
Limit if the limit is a function
Can MMA find limits if the limit can be expressed as a function?
Example:
$$\lim_{x \to \infty}\frac{\Gamma\left(\frac{x+1}{2}\right)}{\Gamma\left(\frac{x}{2}\right)} =\sqrt\frac{x}{2}=\infty$$
$\\\\$
...
-2
votes
0answers
34 views
Write some expressions of the integral
I am trying to apply the Hamilton principle and the final part is the integration. then I should pick some parts only in sperate equation. for example.
The full equation is ...
4
votes
3answers
229 views
Question about plotting a curve and tangent lines
This is a Mathematica question.
I have a function $y=x^3$. “Fun1” is any point on the curve. At the point Fun1, draw a tangent line at that point to the curve.
At another point where the curve and the ...
2
votes
1answer
46 views
How to convert a Piecewise function in a HeavisideTheta function?
I want to convert a Piecewise function in a HeavisideTheta function in order to correctly evaluate its derivatives at the point of abrupt change and then integrate the result along the axis. How can I ...
0
votes
1answer
46 views
Assuming two integers are odd
Is there a way to assume both n and k are odd in Mathematica?
Assuming[{n > 0, k > 0}, Exp[-I*(\[Pi]/2)*(n^k)] // FullSimplify]
n=1,3,5,7,...
k=1,3,5,7,...
...
1
vote
0answers
54 views
All double integrals produce error [closed]
I am a beginner to the Mathematica community; however, for my Multivariable Calculus class I have made a number of double integrals that have worked successfully. Today, while working every single ...
0
votes
1answer
46 views
Find n-th derivative of the function, display it and then evaluate it at a point of choice
What would be the correct syntax to find the order derivative "$n$" in MMA, and to be able to evaluate it in a certain point.
We ask for an example ;
Find the order derivative 2 and evaluate ...
2
votes
2answers
87 views
Can't compute the Integral
I tried to calculate an integral with the function Integrate, but it runs for a long long time without any answer. I have been checking the integrand and it seems ...
1
vote
3answers
130 views
How to interpret these integrations with DiracDelta?
Let us consider the double integral of DiracDelta[y-x^2] over the triangle
with vertices at $(-1,0),\,(-1,2),\,(1,0)$.
Mathematica calculates it as an iterated ...
0
votes
1answer
48 views
Integral involving orthogonal functions (quantum harmonic oscillator eigenstates)
I have a question about the capabilities of the Integrate command for general parameters.
We know that there is a system of functions:
...
-1
votes
1answer
91 views
How to understand these integrals with DiracDelta?
Namely,
Integrate[DiracDelta[y - x^2, z], {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]
(*2 Sqrt[2]*)
and
...
2
votes
2answers
113 views
Exporting a FEM mesh from a parametric surface
How is it possible to export a mesh for suitable finite element analysis (such as Abaqus) from a parametric surface expressions? I'm working on this kind of surface:
...
3
votes
3answers
637 views
Why doesn't Mathematica integrate this?
I am trying to do this integral in Mathematica:
f[x_] := A*Exp[-x^2*M/(2*kb*T)]*DiracDelta[v - Abs[x]]
Integrate[f[x], {x, -Infinity, Infinity}]
It just writes out ...
0
votes
3answers
50 views
How to calculate the derivative of the solution of DSolve?
It should be a particularly straightforward problem to solve. However I cannot manage to do it. I get a solution from a differential equation via DSolve. I just want to calculate now the derivative of ...
0
votes
1answer
81 views
Find the probability (relative volume) of a certain 4-ball with respect to Hilbert-Schmidt measure
Let us consider the set of points {x,y,z,1-x-y-z} and impose the strict ordering constraint
...
2
votes
2answers
157 views
Unexpected Indeterminate result from evaluating a limit [closed]
Consider
$\qquad \underset{h\to 0}{\text{lim}}\dfrac{\sqrt[4]{h+x}-\sqrt[4]{x}}{\sqrt{h+x}-\sqrt{x}}$
Here is what I get when I evaluate it Mathematica:
When I calculate it by hand and in other ...
