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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.

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How to calculate a definite integral with a parameter

I am trying to calculate the following definite integral with the parameter H. So my result would like to be a analytical one with the parameter H. For example for the integral NIntegrate[ax, {x, 1, ...
Dinos Volanis's user avatar
2 votes
2 answers
58 views

`Integrate` gives an imaginary part for a 1-d definite integral of a real-valued function

I'm using Integrate to evaluate an integral with known result: $$\int_0^\pi \frac{\cos(n \theta)-\cos(n \theta_0)}{\cos(\theta)-\cos(\theta_0)} d\theta = \frac{\pi\...
Jie Zhu's user avatar
  • 573
0 votes
1 answer
49 views

About a double integral [closed]

I try to use walfram mathematica to compute a double integral, my code is ...
Vanellope's user avatar
2 votes
1 answer
71 views

Generate variables in multiple integral

I want to do a multiple integrate with n variables. When I change the value of n, I do not want to rewrite the variables in the integral manually like here: ...
Zsombor's user avatar
  • 185
3 votes
1 answer
140 views

Mathematica gives zero for non-zero double integral?

Consider the following integral $$\int_{-\infty}^{\infty} dy \int_{-\infty}^{\infty} dx\, \frac{1}{(xy+i)(x+y-i)^2},$$ where $i$ is the imaginary unit. I can evaluate this integral analytically using ...
jkb1603's user avatar
  • 155
-1 votes
0 answers
33 views

Symbolic derivatives [closed]

f(t)=a(t)*b(t) How do I make make Mathematica output df/dt like this f'(t)=a(t)*b'(t)+a'(t)*b(t)
sato's user avatar
  • 99
4 votes
0 answers
80 views

How to obtain the boundary of a two-dimensional ParametricRegion surface in order to apply Stokes' theorem to compute surface integrals?

On the help page of the SurfaceIntegrate, an example of Stokes' theorem is listed: Compute the Curl ...
lotus2019's user avatar
  • 2,131
1 vote
2 answers
111 views

Contour integral with radius infinite [closed]

How can I get compute a contour integral of the function $f(z)=\exp(i z)/z$ in the upper circle with center in $(0,0)$ and radius $R$? I want verify that $\lim_{R\to \infty}\int_C f(x)=0$ in ...
eraldcoil's user avatar
  • 203
1 vote
1 answer
40 views

Issue with FullSimplify in StirlingS2 definition

I have previously asked a question about a problem simplifying an expression in Mathematica. The solution was to expand the definition of StirlingS2. This time, I ...
Cardstdani's user avatar
0 votes
1 answer
37 views

Problem calculating mean of probability distribution

I have a discrete probability distribution where $P(X=x)=(Factorial[n]/(n^x))*StirlingS2[x-1,n-1]$. So, when trying to calculate its mean with the following property: $\mu = \sum_{i} x_i \cdot P(x_i)$,...
Cardstdani's user avatar
3 votes
3 answers
291 views

Parabola from a focus and a directrix

The code below is an attempt to obtain the graph of a parabola from two pieces of information: a focus and a directrix. I am not able to get the correct graphical shape of the parabola. I appreciate ...
Rubens Vilhena Fonseca's user avatar
1 vote
0 answers
70 views

How can I ask Mathematica to give the explicit real form of the given function?

In part of my calculations, I obtain this expression which contains the imaginary unit I but I expect that this expression might be real (from the comments below, ...
MsMath's user avatar
  • 175
4 votes
2 answers
113 views

Questions About the FunctionExpand Function

Today, while helping someone solve a problem, I encountered an issue with the Abs function in their expression. I needed to derive the ...
我心永恒's user avatar
  • 1,562
9 votes
3 answers
1k views

Taxicab Geometry

According to taxicab geometry, there are 1226 possible paths from A(2,5) to B(7,9), all with a distance of 9 units, |2-7|+|9-5|=9. I wanted to write a code where I could be obtaining the plots of some ...
Rubens Vilhena Fonseca's user avatar
0 votes
1 answer
48 views

Trying to find divergence of 4-D second rank tensor

I want to find a divergence of a 2-rank 4-dimensional tensor(one time and three spherical spatial), and the following is the code I've tried. : ...
Deven Desai's user avatar
1 vote
3 answers
134 views

Maximum value of a constant in a function [closed]

I'm trying to find the maximum $B$ of the following function: ...
Dayzk's user avatar
  • 121
0 votes
1 answer
56 views

Convergent Taylor series unrecognized by Sum

I am trying to understand why Sum does not recognize a particular Taylor series as convergent. I have defined a function 'series' like this, that computes the Taylor series of a function 'f' at 'x', ...
Glenn Welch's user avatar
0 votes
0 answers
48 views

performance of the NDEigensystem and DEigensystem

I can't find any result and I can't understand what is going wrong. Any help please? My code is: ...
HarrisModel's user avatar
5 votes
1 answer
58 views

Integration of function in Mathematica where the variable has dimension

I want to Integrate a function $f(x)=\dfrac{1}{x-a}$ where both $x$ and $a$ have the dimension of length. After doing the integration in Mathematica it is returning the solution $\log(x-a)$. But here ...
darkphysics's user avatar
1 vote
2 answers
80 views

How to demonstrate the acceleration using spherical coordinates and spherical unit vectors?

I've been trying to use Mathematica to demonstrate using spherical coordinates and unit vectors the acceleration for a particle moving in a sphere. Nevertheless, I'm actually not that skilled in ...
not_aphysicsdr's user avatar
3 votes
3 answers
200 views

Finite Differences:

I am having difficulty implementing finite differences in the correct columns of my code. ...
Rubens Vilhena Fonseca's user avatar
3 votes
1 answer
64 views

Integral of interpolation function is not evaluated

I am having a misunderstanding with Mathematica about integration of InterpolatingFunction. Consider this example: ...
atapaka's user avatar
  • 3,954
0 votes
0 answers
36 views

Regarding Poincare section

I got a code from Mathematica to plot the Poincare section and in this code, so many initial conditions are taken at a time. The link and the code is given below. link ...
Arssat's user avatar
  • 81
0 votes
2 answers
57 views

How to find value of parameter for given number of maxima simpler?

Let us consider a function f[x_,a_]:=Exp[x]*Sin[a*x/5].The question is: how to find the minimum value of a parameter a > 0 s....
user64494's user avatar
  • 26.4k
0 votes
2 answers
71 views

Comparing Closed-form to Numerical Integral Result

When I numerically calculate this integral NIntegrate[(1/2)*Log[1 + Sin[x]]^2, {x, 0, Pi}] The result is $0.416217488896557$ and I verified it using another tool....
Moo's user avatar
  • 3,292
0 votes
1 answer
106 views

Analytically solving this second order ODE

I try to solve this second order differential equations to get $\phi$: $$ 4 \Psi \left( \ddot{\phi}_0+ \frac{a^2}{2\phi_0}\dot{\phi}_0 \right) = -\ddot{\phi}+ \left( \frac{a^2 \mathcal{H}}{2\phi_0} ...
Dr. phy's user avatar
  • 287
0 votes
1 answer
129 views

Mathematica code to compute a constant

I am reading an interesting paper One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational by Zudilin. We fix odd numbers $q$ and $r$, $q\geq r+4$ and a tuple $\eta_0,\eta_1,...,\eta_q$ of positive ...
Max's user avatar
  • 145
-1 votes
0 answers
46 views

change variables

I've got this integral. (1/(x2 - x1))*Integrate[\[Gamma]/(x^(1/2)*(x/t + \[Gamma]/x^(1/2))), {x, x1, x2}] ...
lia's user avatar
  • 345
2 votes
3 answers
146 views

Finding $\frac{\cos(b)}{\cos(a)}$ given $\cos(x) e^{i y} = \frac{\sin(a)}{\sin(a+b)}$ and $-i \sin(x) e^{i y} = \frac{\sin(b)}{\sin(a+b)}$

I have real $x$ and $y$, and I have the following implicit definitions of (complex) $a$ and $b$: $$\cos(x) e^{i y} = \frac{\sin(a)}{\sin(a+b)}$$ $$-i \sin(x) e^{i y} = \frac{\sin(b)}{\sin(a+b)}$$ I ...
user196574's user avatar
2 votes
0 answers
37 views

Take symbolic derivative of summation expression and display as unexpanded sum

My main problem here is two-fold: Take symbolic derivative of summation expression Stop summations from being "unrolled"/expanded, e.g., displayed as the sum of terms I also have some ...
ImagineBaggins's user avatar
0 votes
1 answer
64 views

Clear Guidelines for Symbolic Calculation With Units?

The following notebook performs a relatively simple physical calculation interacting position, velocity and acceleration of two charged point particles according to Weber electrodynamics.It is simple ...
James Bowery's user avatar
1 vote
0 answers
37 views

Integral within another integral [duplicate]

I have to evaluate the following integral: $I(k) = \int^{42}_{0} dt \hspace{0.1cm} 3t^3*e^{i \int_{0}^{t}dx( x^2 - \sqrt{x^4+k^2/x}) }/\sqrt{t^4+k^2/t}$ The answer in : Iterated integral numerically ...
Antonis Kyriazis's user avatar
2 votes
2 answers
103 views

Limit with integral [closed]

I have this Limit: it's indeterminate. How can it be solved? ...
lia's user avatar
  • 345
4 votes
0 answers
92 views

Weird behavior of derivative D[] function in v11

Bug introduced after version 9.0.1, in or before version 11.0, fixed before 12.3. Recently I noticed that a code developed in v13 was giving unexpected errors about the formatting of matrices in v11 (...
Hans Olo's user avatar
  • 1,843
2 votes
2 answers
147 views

Wolfram|Alpha is unable to evaluate this improper integral

I want to solve this integral $$\int_{0}^{\frac{\pi}{2}} e^{-(\pi \tan(x) - 1)^2} \, dx$$ I tried Wolfram alpha but it is unable to evaluate I tried this code ...
Wizard's user avatar
  • 131
2 votes
3 answers
210 views

Solving divergent Integral

I want to solve this integral. using Integrate I get it done, but the problem is it results in complex values, which is incorrect for my problem (has no physical meaning). I'd like to know if there's ...
lia's user avatar
  • 345
0 votes
0 answers
53 views

Speeding up the output of DSolveChangeVariables

I am trying to change the variable in a differential equation using the above mentioned function. This is what I did: ...
RKN's user avatar
  • 1
0 votes
3 answers
73 views

Split integral domain function

Sometimes we would like to split the domain of a definite integral into two (or more) regions, for instance to exploit symmetry or otherwise produce two (or more) simpler integrals. I can do this &...
David G. Stork's user avatar
7 votes
2 answers
344 views

Wrong result for simple real-valued integral (spurious imaginary part)

There's a question on math SE (question 4879248) about this integral: ...
Jos Bergervoet's user avatar
1 vote
1 answer
126 views

Bifurcation Diagram for x' = (rx) - sinx

I solved for finding the fixed points analytically for various ranges of u for x'[t] = (ux) - sinx for u = 0 0 <u <<1 u>1 0>u>-infinity and its a very complicated bifurcation ...
CuriousMind's user avatar
0 votes
1 answer
54 views

Finding value of a function at limit zero

I want to evaluate the below function at limit zero. I tried with a function which has double differentiation for which it is giving me a finite value. For triple differentiation it is consistently ...
Anshul Bokade's user avatar
0 votes
1 answer
65 views

Gradient of tensor expressions

I would like to compute gradients of tensor expressions without having to instantiate particular tensors and for arbitrary sizes. Example 1 : For example, let's say I want to minimize $C=\sum_j(\sum_i ...
Nichola's user avatar
  • 101
0 votes
1 answer
40 views

Get explicit formula after matrix derivation with Mathematica

I want to calculate the derivative of a matrix with respect to a vector with mathematica, and I would like to know if it is possible to have a formula as an answer instead of an expanded matrix. For ...
ZchGarinch's user avatar
3 votes
1 answer
106 views

Asymptotic integral expansion at infinity [closed]

Define for all $n\in\mathbb{N}$, a definite double integral, $$I_n= \int_{0}^{1}\int_{0}^{1}\left(\frac{x^2(1-x)y^2(1-y)}{1+x^2 y^2}\right)^n\frac{\cos((2n+1)\tan^{-1}(xy))}{\sqrt{1+x^2y^2}}\ dxdy$$ ...
Max's user avatar
  • 145
7 votes
1 answer
150 views

Incorrect result for Integrate[] over Region

I was doing a calculation that involved integrating rational functions over a triangular region, and eventually noticed some of my results didn't make any sense. After some investigating, I was able ...
smish's user avatar
  • 51
2 votes
1 answer
38 views

Nested NIntegrate with limit variable dependance

Hope you are doing great! I am trying to solve a double Integral of a function let's say f(w,q). My upper and lower limits are ...
Ioannis Polopetrakis's user avatar
1 vote
1 answer
37 views

Not able to integrate function involving scalar product

For given $h=0.2,D=1.5$, let $w_{i}(x):=\frac{1}{\pi D}\exp^{-||\frac{x-hi}{\sqrt{D}h}||^{2}}$ where $x\in \mathbb{R}^{2}$ and $i\in I \subset \mathbb{Z}^{2}.$ For $x\in \mathbb{R}^{2}$ ,let $v(x):=-...
chintan's user avatar
  • 15
1 vote
3 answers
169 views

Weakness in Reduce and Solve and FindInstance

In 14.0 on Windows 10 I solve a trig equation $$2 \cos ^{-1}(\sin (\pi x))=\pi \cos \left(\sin ^{-1}(x+1)\right) $$ by ...
user64494's user avatar
  • 26.4k
1 vote
1 answer
65 views

How can I find the amplitude of sine that produces a given arc curvature?

I am trying to find the amplitude a of a sine function f[] that results in a certain arc curvature. I know how to calculate the arc curvature by integrating over ...
Mikl's user avatar
  • 101
3 votes
1 answer
100 views

Problem with calculation of Lyapunov exponent

The code given by Chris K for Lyapunov Exponent does not work and gives lot of errors for the dynamical system given in equation(2) of this paper The dynamical equations: ...
Arssat's user avatar
  • 81

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