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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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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
98 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
205 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
67 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
  • 4,006
0 votes
0 answers
41 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
  • 187
0 votes
2 answers
60 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
  • 27.3k
0 votes
2 answers
72 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
  • 3,388
0 votes
1 answer
108 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
134 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
  • 155
2 votes
3 answers
150 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
41 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
67 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
  • 347
4 votes
0 answers
97 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
  • 1,838
2 votes
2 answers
154 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 ...
Mods And Staff Are Not Fair's user avatar
2 votes
3 answers
215 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
  • 347
0 votes
0 answers
56 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
-2 votes
3 answers
93 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
355 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
2 votes
1 answer
149 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
1 vote
1 answer
57 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
72 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
42 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
108 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
  • 155
7 votes
1 answer
161 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
39 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
174 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
  • 27.3k
1 vote
1 answer
66 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
115 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
  • 187
3 votes
1 answer
172 views

How to use Mathematica functions ArcLength and ArcCurvature?

I want to use Mathematica to find the length of a curve and the sum of angles you would turn back and forth when travelling along that curve. To clarify, the angle I am looking for is the sum of all ...
Mikl's user avatar
  • 101
0 votes
1 answer
65 views

How do I differentiate this in Mathematica? [closed]

I have the following expression: $$v=-r\omega \left( \sin\theta + \frac{r\sin(2\theta)}{2l \sqrt{l^2-r^2\sin^2(\theta)}}\right).$$ I need to find $\frac{\rm dv}{\rm d t}$, given that $\frac{\rm d\...
Himanshu Manglik's user avatar
4 votes
4 answers
554 views

Dealing with derivative of noisy experimental data

I have the following (time, position) dataset ...
MOOSE's user avatar
  • 159
0 votes
0 answers
70 views

Problem with Integrate

I am trying to compute the Fourier expansion coefficients by Integrate. ...
Ren Witcher's user avatar
2 votes
0 answers
181 views

How to plot the sum of this function series?

Let us consider the sum of a function series $$ \sum _{n=1}^{\infty } \frac{z^n}{\left(z^n+1\right)^n}.$$ This series absolutely converges if Abs[z] < 1 or ...
user64494's user avatar
  • 27.3k
3 votes
0 answers
42 views

Cannot add a constant coefficient to LineIntegrate

I'm quite confused on how you're supposed to use constant coefficients in Mathematica integrals. The upvoted and accepted answer on Mathematics stackexchange (https://math.stackexchange.com/a/48021/...
Cedric Martens's user avatar
5 votes
1 answer
259 views

Quantum Field Regularization: Choice between ExpIntegralE and Gamma for Casimir Effect

For the Casimir effect with exponential regularization, we compute the vacuum energy between the plates (somewhat simplified) with: $$\omega = c\ \sqrt{q^2+k_z^2}$$ $$ E = \sum_{k_z=n\pi/a} 2 \int\...
Jos Bergervoet's user avatar
5 votes
2 answers
321 views

Integrate has issues when integrating the general form of a trigonometric integral but not specific instances

I'm trying to solve with Mathematica the following integral for $m$ a positive integer $$s=\int_{0}^{1/2}\frac{\sin^4(\pi\nu m)}{m^2\sin^2(\pi\nu)}\mathrm{d}\nu$$ which should yield $1/(4m)$ (I ...
Massimo Ortolano's user avatar
1 vote
0 answers
96 views

Differentiation of Parabolic Cylinder Functions and Hermite Polynomials w.r.t to Order

When I evaluated (ver. 12.3) parabolic functions below in the vanishing order limit: $u \rightarrow 0$, I got the following: ...
user91411's user avatar
  • 400
4 votes
1 answer
189 views

How to find a closed-form expression for this integral depending on parameter?

In 14.0 under Windows 10 I try to find the improper integral $$\int\limits_{\sqrt{1-\sqrt{1-\psi }}}^{\sqrt{1+\sqrt{1-\psi }}} \frac{1}{r^2 \sqrt{-r^4+2 r^2-\psi }}\,dr$$ under the assumptions $\psi &...
user64494's user avatar
  • 27.3k
3 votes
1 answer
116 views

Define a function whose variable is differential operator

I would like to act with a differential operator $D_x = x \partial_x^2+3\partial_x$ on a function $g(x)$ to compute something like $$ ((D_x)^2 +D_x) g(x) $$ Clearly, in this simple example, this does ...
bnado's user avatar
  • 413
0 votes
1 answer
77 views

Conformal Mapping Function and Scaling Factor

I am having problems determining a scaling factor for a conformal mapping function. The plan is to map the upper half plane into a rectangle (Schwarz Christoffel Transformation) to determine the ...
tommowic's user avatar
4 votes
2 answers
186 views

How to improve the following code to get rid of the warning messages?

I have to solve the following initial Value problem $$y'=\frac{2xy}{y^2-1}, \quad y(2)=1$$ so, I wrote the following code to solve it ...
Athanasios Paraskevopoulos's user avatar
2 votes
0 answers
174 views

How to perform the following deduction symbolically?

$$i \frac{d}{dt}a_n = (a_{n+1} + a_{n-1}) + |a_n|^2 (a_{n+1} + a_{n-1}), \; n \in \mathbb{Z}$$ In the above, $a_n := a_n(t)$. Consider $P = \sum\limits_{n}g(|a_n|^2)$ where $g$ is some function to be ...
KZ-Spectra's user avatar
8 votes
2 answers
193 views

Numerical integral does not agree with analytic integral

I am trying to evaluate a function, that I've now reduced to its minimum (not) working example. Unless I am doing something very wrong, it appears that NIntegrate ...
poupou's user avatar
  • 97
0 votes
0 answers
146 views

Unable to compute integral on implicit region

I am new to Mathematica. I need to deal with the following computation ...
Lorenzo Cecchi's user avatar
4 votes
1 answer
98 views

Numerical Solution for a Non-Linear Functional Fractional Differential Equation (FFDE)

I tried solve non-linear Functional-Fractional Differential Equation (FFDE) with this method, but it works on only for range: $x\in \{0,1\}$. I what extend the solution range for example for general ...
Mariusz Iwaniuk's user avatar
4 votes
3 answers
272 views

Setting up a double integral over a polar region

Clear["Global`*"]; f[x_, y_] := 9 - x^2 - y^2; Integrate[f[x, y], {x, -1, 1}, {y, -Sqrt[1 - x^2], Sqrt[1 - x^2]}] Integrate[f[x, y], {x, y} ∈ Disk[]] ...
Syed's user avatar
  • 56k
2 votes
2 answers
112 views

Interpreting the output of double integral over a Circle

Clear["Global`*"]; f[x_, y_] := 9 - x^2 - y^2; Integrate[f[x, y], {x, -1, 1}, {y, -Sqrt[1 - x^2], Sqrt[1 - x^2]}] Integrate[f[x, y], {x, y} ∈ Disk[]] ...
Syed's user avatar
  • 56k