All Questions
Tagged with calculus-and-analysis functions
270 questions
1
vote
2
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102
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Generate n tables of values for functions
After searching for a long time, I can't find how to do what I need with some bold header style.
I need to generate n tables of values for linear functions (f(x)=mx+n), where x varies from -6 to 6, ...
- 309
1
vote
1
answer
90
views
How to express the argument through the function?
I would like to express argument $d$ through $f$ and $B$ and to get $d(f,B)$
$$f(d,B)=B\left(\left(\frac{1}{4}-\frac{d}{B}\right)\left( 1-\left(1- e^{-30d/B} \right)^8\right)+\frac{2/B}{3+1/B^2}\left(...
- 1,893
0
votes
1
answer
55
views
Can someone please explain where I am going wrong in the given argument? Is it obvious that $f(m,s)>0$?
I have a two-variable function $f(m,s)$ for real $m>0$ and $s>0$, and as the first picture shows, it seems that it is always positive; on the other hand, I can easily find the minimum of $f(m,s)$...
- 349
0
votes
1
answer
76
views
Is there any hope to compute analytically $y=f(x)$ for which $g(x,y)=0$?
I have a two-variable function $g(x,y)$ with $0<x\leq\frac{\pi}2$ and $\frac32<y<5$. I am looking for $y=f(x)$ for which $g(x,y)=0$. Using ContourPlot
<...
- 1,159
0
votes
0
answers
91
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Functions for translating a vector from one coordinate system to another
I have a vector $\vec{H}$ with components in Cartesian coordinate system $(x,y,z)$: $\vec{H}=(0,0,H)$. I would like to obtain coordinate of this vector in Spherical coordinate system $(r,\theta,\phi)$....
- 1,893
7
votes
1
answer
308
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How to use Slater Type Orbitals as a basis functions in matrix method correctly?
This question is a continuation of my previous series of questions about basis functions.
I would like to find the minimum energy of Coulomb potential motion using matrix method.
$H=-\frac{1}{2}\Delta-...
- 1,893
0
votes
1
answer
104
views
How to compute the residue of $f(z)=\frac{n/z}{z^{n}-1}$ to be $-n$ at $z=0$? [duplicate]
How to get residue of $f(z)=\frac{n/z}{z^{n}-1}$ with correct residue of $-n$ at zero?
It works it out just fine at 1 with:
Residue[(n/z/(z^n - 1)), {z, 1}]
- 343
0
votes
1
answer
55
views
FunctionDomain and FunctionRange for x^2/x returns "True"
I'm very concerned. As far as I know, the output should be:
$x < 0\ ||\ x> 0$
$y < 0\ ||\ y> 0$
0
votes
1
answer
124
views
How to get rid of curly brackets from a function output? [closed]
The following codes of ode provides solutions for x1(t),y1(t),and v(t) as interpolating functions.
...
- 99
0
votes
1
answer
94
views
How to use interpolating function for function composition?
The following codes give solutions of x(t),y(t), and v(t) as interpolating functions. How to transform y(t) to a regular function so that it can be used for function compostion of y(z(T))? Z(T) is a ...
- 99
0
votes
1
answer
44
views
0
votes
0
answers
100
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Maximization Problem
I am trying to find the solution of the following problem.
$ \max_{n_{\in [1,M]}} \frac{n \left(\frac{k (n-2 (\rho -1) \tau )}{\frac{k n (n-2 (\rho -1) \tau )}{2 (n+1)^2}+1}-2 \rho (\tau -1)\right)}{...
- 70
1
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1
answer
220
views
5
votes
1
answer
226
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Series Converges or Diverges?
I am running MMA 13.1.0.0 on Windows 10 - x86.
Is there any way to get Mathematica to conclude that this sum converges (maybe it needs some additional input)?
...
- 3,464
0
votes
0
answers
33
views
Defining parameter as function without losing properties of the derivative
I have built a code that is later on solved dynamically depending on values I set using Manipulate while plotting. However, I came across a problem I cannot resolve. So, I defined ...
1
vote
2
answers
105
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How to ask Mathematica to rewrite the larger arguments of sine function as a smaller number which is multiple of $\frac{2\pi a}{11}$
I have a trigonometric function $Exp$ where $\{f,g,h,k\}$ are some parametric functions, and $a\in\mathbb{N}$ and $x>0$.
$$ Exp=f \cdot \sin \left(\frac{58 \pi a}{11}+x\right)+g\cdot \sin \left(\...
- 1,159
0
votes
1
answer
73
views
What is the most efficient/optimal way to simplify the given function? Does the given code need more assumptions?
I have a very long function for $\{x,b\}\in\mathbb{R}$ and $n=\{1,2,3,4,5,6,7,8,9,10\}$; here, I have only mentioned a short part of that. The function is a sum of the complex exponentials (a picture ...
- 1,159
2
votes
2
answers
160
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Simplifying a sum of complex exponential terms
I have this function for $n=\{1,2,3,4,5,6,7,8,9,10\}$. Is there any hope to significantly simplify this function (make it shortened) for general $n$? I use Simplify
...
- 1,159
1
vote
1
answer
177
views
Results of Limit unclear and given as an interval
When we do this limit
Limit[E^x*(1 + Sin[x]), x -> Infinity]
The result is
Interval[{0, \[Infinity]}]
Is this saying ...
- 3,464
1
vote
4
answers
114
views
Simplifying a function to get rid of fractional powers of $-1$
I have the following function for $x>0$.
...
- 749
2
votes
1
answer
203
views
Evaluate Tricky Multivariable Integral
I'm trying to model an experiment for a paper which includes an integral that should be no problem for mathematica but it refuses to integrate it. The integral I need to evaluate is as follows
...
- 61
0
votes
0
answers
48
views
How to find the sequence function $f(n,x)$ of the three given functions?
I have the three functions $f(2,x)$, $f(3,x)$ and $f(4,x)$ where $x>0$
...
- 749
0
votes
2
answers
68
views
Additional line in the Plotting
I'm trying to plot a function, the problem is that the plot contains additional lines which originate from the solution itself, but at the same time removing the solutions will delete a whole portion ...
0
votes
0
answers
63
views
Using discrete distribution to fit continuous distribution and then reproduce the same discrete distribution, all on the same Plot
I'm using the discrete distribution function to fit the continuous distribution by method of moments, and then, trying to reproduce the same discrete distribution function.
The data used to plot the ...
0
votes
2
answers
120
views
How to take the derivative with respect to a function with more than one variable?
I have a function that includes another function inside. I want to know the derivative at every point x. I have spent a lot of time trying to figure out how to do this, but I am very lost. I have ...
- 263
1
vote
1
answer
95
views
Value of allegedly infinite limit is different for different values of the variables
I have a $5$-variables function $f(x,y,z,u,v)$ and I want to compute the limit as $x\to\frac{3\pi}u$; using this code for general values of parameters, Mathematica gives the answer ...
- 153
0
votes
0
answers
58
views
Derivatives with respect to vector components
I am trying to work with functions of arrays, I tried the following:
f[x_] := x[[1]]^2 + x[[2]]^2 + x[[3]]
D[f[x], x[[1]]]
and got
...
- 101
3
votes
4
answers
155
views
How to get mathematica to work out residues of $f(z)=-\left(\frac{z-1}{z+1}\right)^2\frac{2n/z}{z^{2n}-1}$?
Using the function,
$f(z)=-\left(\frac{z-1}{z+1}\right)^2\frac{2n/z}{z^{2n}-1}$,
should give residues as follows:
$
\begin{align}
\
&\left(\operatorname*{Res}_{z=0}(f(z))+\operatorname*{Res}_{z=-...
- 343
0
votes
1
answer
117
views
Derive a symbolic expression
Sorry, I am new to Mathematica and this problem is doing my head in. I have the code in the picture below, I would expect Mathematica to do the derivative wrt q_1 when I write U'[q_1]. However, it ...
- 125
3
votes
1
answer
99
views
Define an operator for long equations
I'm trying to workout a long expression with derivations, the thing is I can't seem to transfer this problem to code.
What I need is a operator $D = l^\mu \frac{\partial}{\partial x^\mu} $ where $l^\...
- 790
1
vote
3
answers
427
views
How to linearize function of functions?
From the post, I know how to linear a simple polynomial function of several independent variables.
For example, for two variables a1=q1+eps*q1 and ...
- 137
3
votes
1
answer
107
views
Can I plot a function in terms of its derivatives?
I have sign conditions on the partial derivatives of a function of two variables $f(x,y)$ and its cross-derivative, but I do not know the function itself. Can I visualise a prototype of such function?
- 155
2
votes
1
answer
235
views
How FunctionConvexity is implemented in Wolfram Mathematica?
I am wondering how FunctionConvexity was implemented in Wolfram Mathematica.
I am trying to prove the convexity of the function $A(v)$:
$$ A(v) = -\dfrac{k-1}{\...
- 81
1
vote
2
answers
75
views
Why the animation of a function gives different results from the integral?
My function is:
A1[B_, x_, t_] := (AiryAi[B*(x - (B^3*t^2)/4)])^2
(B is a constant) and if I use "Manipulate" :
...
- 49
2
votes
1
answer
285
views
Biot-Savart Integral
I want to calculate the magnetic field of a finite wire of current along the z axis. I assume a frame of reference like the one in Fig. below:
It is a classical problem with a well known solution for ...
2
votes
2
answers
91
views
Calculation of composite integrals
I am facing trouble calulating the following integrals. Could you give me any advice?
My code is the following:
...
- 49
0
votes
0
answers
211
views
Multivariate Pade approximant
Does Mathematica generate multivariate or just two-variate Pade approximant? If so, what is the generating command?
- 179
0
votes
0
answers
67
views
Is it possible that NSolve gives the roots that the function is not (well-)defined at those points? (an example is given)
I have this function for reals values of $x$ for $2<x<3$.
$$f(x)=(3 \pi -2 x)^2 \sin \left(\frac{1}{2} \left(\csc ^{-1}\left(\frac{4 \pi (\pi -x) \csc \left(\frac{\pi ^2}{\pi -x}\right)}{4 x^2-...
- 749
1
vote
1
answer
374
views
Is there any alternative for NSolve or Solve to obtain all the roots of the given function?
I have this function for reals $0<x<\pi$.
$$f(x)=(3 \pi -2 x)^2 \sin \left(\frac{1}{2} \left(\csc ^{-1}\left(\frac{4 \pi (\pi -x) \csc \left(\frac{\pi ^2}{\pi -x}\right)}{4 x^2-8 \pi x+5 \pi ^...
- 749
2
votes
2
answers
212
views
How can I make sure that there are real roots for the given function? Can I trust the plot only?
I have this function
$$f(x)=(\pi -2 x)^2 \sin \left(\frac{\pi ^2}{2 x-2 \pi }+\frac{1}{2} \csc ^{-1}\left(\frac{4 \pi (\pi -x) \csc \left(\frac{\pi ^2}{x-\pi }\right)}{4 (\pi -x)^2+\pi ^2}\right)\...
- 749
0
votes
2
answers
238
views
How plot the domain of multivariable function? [closed]
I want to get and plot the domain of the following function with mathematica :
$$Arccos(xy)$$
Any idea ?
- 153
0
votes
0
answers
79
views
Integral of functions within functions
I define the function Rho, use it in an integration command, store that result as a new function M, then write functions P and Rho1 in terms of M and Rho, and finally integrate Rho1 and store that as ...
- 1
3
votes
1
answer
485
views
Setting a function equal to an integral
I am trying to solve for the constant of integration in simple calculus problems.
v[t_] := Integrate[-0.08 t, t] + C
v[t]
gives me
...
- 802
0
votes
2
answers
221
views
Is it possible to calculate the desired area analytically?
I have the three two-variable curves $f,g,h$ with $0\leq x\leq \frac {\pi}{2} $ and $0 \leq y \leq \pi$
I use ContourPlot as
...
user80186
6
votes
2
answers
166
views
Efficient computation of Hopf invariant
I am trying to check using Mathematica the following result:
$$-\frac{1}{4\pi^2}\int_{0}^{2\pi}\int_{0}^{2\pi}\int_{0}^{2\pi} \mathbf{F}\cdot\mathbf{A}\;dk_x dk_y dk_z=1,\quad\text{where}$$
$$z_{\...
- 163
0
votes
1
answer
39
views
How to write a function taking limit of multivariables in sequence?
I'm trying to write a function to calculate the limit of a function on a number of variables in sequence.
Here I take a function with four variables x, ...
- 2,111
0
votes
2
answers
65
views
Supremum of a complex periodic signal in symbolic form
For complex periodic signal:
$-\frac{8 T \left(2 T \omega \sin (2 t \omega )-e^{-\frac{t}{T}}+\cos (2 t \omega )\right)}{\alpha ^2 \left(4 T^2 \omega
^2+1\right)}$
where $T,\alpha,\omega$ - ...
- 2,494
4
votes
3
answers
302
views
How to find absolute minimum with NMinimize
So I have a trefoil and twisted cubic that are very close to intersecting but do not. I know NMinimize can be used to best approximate the minimum, but it ...
- 91
4
votes
3
answers
307
views
Plotting a parametric function on xy, xz, and yz planes
I'm trying to plot a trefoil with a parametric function in Mathematica. How would I do that? I know I can use Parametric3D to depict all of it but how do I project it on the XY, XZ, and YZ planes?
It'...
- 91
0
votes
1
answer
105
views
