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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4
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1answer
261 views

A complicated boundary value problem leading to third order Eigen sytem [Help in continuing forward] [EDITED]

I have the following elliptic PDE (describing temperature in a plate, w in thermal contact with two fluids h and c): $$\lambda_h \frac{\partial^2 \theta_w}{\partial x^2} + \lambda_c V \frac{\partial^2 ...
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1answer
82 views

Why does this integral not compute?

I have the following set of equations: $$ T_{man} (\phi_{max}, p_{max}) := \frac{\phi_{max}}{p_{max}} $$ $$ \dot\phi_{ac} (T_{trig}, \phi_{max}, p_{max},t) := \begin{cases} 0 & t<T_{trig} \\ ...
1
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1answer
24 views

Create vector/matrix function from derivatives of scalar functions

I am attempting to plot the determinant of a Jacobian matrix that is defined by deriving scalar functions and combining these derivatives into a matrix function (the Jacobian) and then taking its ...
2
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1answer
78 views

Correcting HeavisideTheta in MM11.3 for generating the same results with UnitStep in MM5.2

The UnitStep was replaced with the HeavisideTheta after the version 6.0 (reference here), but some differences confused me ...
0
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1answer
32 views

Simplification of an integral through product manipulation under the integration symbol

Consider an integral of the form Integrate[ f[a*x] g[c1*z1+c2*z2+c3*z3] h[e*x] k[d1*z1+d2*z2+d3*z3] ,{x,0,1} ,{z1,0,2} ,{z2,0,3} ,{z3,0,4} ] Assume that ...
16
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1answer
302 views

Solver for COVID-19 epidemic model with the Caputo fractional derivatives

As it is known in biological system with memory it would be suitable to use fractional derivatives to describe evolution of the system. In a current version of Mathematica 12.1 there is no special ...
0
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0answers
63 views

3 dimensional Laplacian with 4 non-homogeneous boundary conditions

I have the 3-D Laplacian ($\nabla^2 T(x,y,z)=0$) defined over $x\in[0,L], y\in[0,l], z\in[0,w]$ with four non-homogeneous boundary conditions as follows: $$T(0,y,z)=t_{hi}\tag1$$ $$T(x,0,z)=t_{ci}\...
4
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1answer
86 views

Jacobian Matrix?

I am doing r[psi_, th_, phi_] := {Cos[(phi + psi)/2]*Cos[th/2],Cos[(phi - psi)/2]*Sin[th/2], Sin[(phi - psi)/2]*Sin[th/2], Sin[(phi + psi)/2]*Cos[th/2]} and ...
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0answers
53 views

Integration resulting in imaginary result while solving a boundary value problem

I am trying to solve a boundary value problem involving a three-dimensional Laplacian $\nabla^2T(x,y,z)=0$ on the domain $x\in[0,L], y\in[0,l], z\in[0,w]$. I have six boundary conditions and based on ...
0
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0answers
43 views

Code running in Mathematica 12.0 but not in 11.3

When I run the following code in Mathematica 12.0, it doesn't cause any problems but for Mathematica 11.3 it gives General::munfl error ...
5
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1answer
80 views

How to directly get the TeXForm of each steps from Rubi?

It's easy to read the steps from Rubi, but kind of tired to copy it out of as $\LaTeX$. That's what now I do: Int[x Sin[x], x]//Steps For example,click one step, ...
4
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1answer
57 views

Finding group delay of transfer function

I'm having trouble finding the group delay of a transfer function. I've seen a solved question on here about finding the group delay, but I want to understand why my method doesn't work. Here is some ...
0
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1answer
58 views

`FindRoot` : Root varying wildly with initial guess

I am trying to obtain a plot between two variables related through an equation as follows : ...
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0answers
62 views

Numerical comparison of two integrals and a function :

Consider the following integral: $$S(q)=\int_{x=2}^q\sin^2\left(\frac{π\Gamma(x)}{2x}\right)dx$$ And consider the functions : $$R(q)=\frac{q}{\log(q)}$$ $$T(q)=\int_2^q\frac{1}{\log(x)}dx$$ I ...
3
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0answers
30 views

Integration $\int dx f(x,y)$ by replacing $\int dx f(x,\xi)$ for some transcendental number $\xi$

Sometimes when I'm doing a hard integral $\int dx f(x,y)$ where $y$ is a parameter, I replace $y$ with, say, the transcendental number $\zeta(\pi)$, Mathematica will evaluate it more easily, and I'll ...
2
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1answer
186 views

Find best equation for data and the area under curve

How can I find the best formula that describe the following Figure and also find the area under the curve (the numerical value): The data for the figure can be found here: https://pastebin.com/...
0
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1answer
31 views

FunctionDomain ouput conflict with Limit output

I was just trying to find out the available domain for a function using the following : FunctionDomain[-((I*a*(-1 + E^(2*I*a*Pi)))/(-1 + a^2)), a, Complexes] &...
2
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1answer
68 views

How to study the quasi-concavity of a function

I have the following function: f[y_] = y (k + h (1 - y - x) - t (1 - y - x) x + (1 - y) t (-y + x)) where k, h and t are parameters with values comprehended in ...
1
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1answer
24 views

Assumptions in Integrate not working properly

I have the following code: ...
2
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1answer
71 views

Mathematica can't compute this integral (but can a very similar one)

I am having a hard time to understand why Mathematica can't compute the following integral: ...
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0answers
50 views

Using `NIntegrate` or `Integrate` with unspecified constants

I have a function defined like : g[n_, x_] := ((n + 2)*Cos[π*(n + 2)*x] - Cot[π*x] *Sin[(n + 2)*π*x]) and I want to do the following : ...
3
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2answers
87 views

Two identities involving contour integrals in the presence of a branch point where the integrand explodes, and the Kummer function

I need to understand how to establish two identities. The first is $$ \int_{C} z^{-1-q}(1-z)^{-1-\lambda } dz=\frac{2 \pi \Gamma (q+\lambda +1)}{\Gamma (\lambda +1) \Gamma (q+1)}, q\geq 0, \...
7
votes
3answers
101 views

Function tending to $-\infty$ tends to $+\infty$ in picture given by Plot

I have problems with this function $f(x) = e^{-x}+\ln(x+5\pi)$. I computed the following limit by hand: $\lim\limits_{x\to-5\pi^+} f(x)=-\infty$, which I think is correct. But when I plot this ...
0
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0answers
42 views

Evaluate the indefinite integral

I am trying to solve the indefinite integral with user-defined rules. the integral expression and details are shown below where the P is a function of a,b and c. and I would like Mathematica to ...
1
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3answers
131 views

Solving equations involving integrals

I need to find the value of $z$ for a particular value of $D_c$ (eg. $500$), but $z$ is inside an integral, and I'm not able to use Solve since the integral is ...
0
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1answer
41 views

How to define derivative operation of a series acting on normal function

In some cases, I have to do derivarive of higher order acting on some function successively. Here is a toy example: I have a function named myfunc: ...
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0answers
38 views

Why does Plot[D[x,x],{x,1,10}] throw error? [duplicate]

I am experiencing unexpected behavior from Plot and D, and I would like to understand why. If I try this: Plot[D[x,x],{x,1,...
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0answers
37 views

How can I evaluate $\limsup_{x\rightarrow a}f(x)$ in Mathematica?

The Wolfram MathWorld page for supremum limits doesn't mention if or how $$\limsup_{x\rightarrow a}f(x)$$ is implemented in Mathematica. Is there a way to evaluate expressions of this form? Thanks in ...
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0answers
67 views

Jacobian of Mod function giving zeros as result

Could you please explain the following discrepancy in results ? ...
0
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0answers
32 views

Given measures on sets and on certain Boolean combinations of the sets, can one check their consistency and/or extend them to other combinations?

I have four sets--let us denote them $A_i, i=1,\ldots,4$--of quantum-information-theoretic interest (https://arxiv.org/abs/2004.06745, https://arxiv.org/abs/1905.09228). The set $A_1$ contains the ...
1
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1answer
33 views

Referencing the Component of a vector

If I were to define a vector r = {2, 0} + t*({5, 4} - {2, 0}) >>{2 + 3 t, 4 t} Sqrt[(D[r[1]])^2 + (D[r[2]])^2] How do I properly reference a single ...
0
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2answers
23 views

Check sign of second order condition for different values of parameters

I am facing a maximisation problem, and I need to check the concavity of my objective function. (Actually, quasi-concavity would be sufficient, but I have no idea how to check it). In poor words, I ...
7
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0answers
143 views

Two integrals that should not be equal

Bug introduced in 12.0 or earlier and persisting through 12.1.0 CASE:4539809 I think there is a bug here: ...
1
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2answers
97 views

How Can Take Integration of $exp(- \frac{t}{s}) * \frac{(a+c*m*t+c*u*z)}{s*(a+ r*m*t+r*u*z)} dt$

How could I simplify this equation and take integration? Could you please help me? ...
1
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0answers
103 views

How can I get better results using DSolve?

I am solving my fourth-order differential equation by using DSolve. When I solved it gives me an error related to precision. How can I improve my results and get better output? Any help will be ...
0
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0answers
34 views

Finding the volume by rotating the region bounded by the curves $y=\sin(x)$, $y=0$, $x=0$, $x= \pi$ about $y=-1$

I would like to find the volume of the region obtained by rotating the region bounded by the curves $y=\sin(x)$, $y=0$, $x=0$, $x=\pi$ about $y=-1$. Calc 2 wasn't a strong suit of mine, so this ...
0
votes
1answer
48 views

Why is Mathematica giving this answer for the derivative of 2^x? [closed]

I'm trying to use Mathematica to take the derivative of 2^x with respect to x. It's giving me the attached answer, which is not correct. Am I doing something wrong? Why is it giving this answer? Edit:...
1
vote
1answer
108 views

Convergence of integral [closed]

I'm trying to calculate analytically the integral below $$ I = \int_{-\infty}^{+\infty} -\frac{2 \mathrm{e}^{k^2/2 + 5} k^2 (k^2 + 10)}{(\mathrm{e}^{k^2/2 + 5} - 1)^2} \mathrm{d}k $$ I've already ...
0
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0answers
29 views

Can't find a way to numerically evaluate integral with singularity

Consider this function: $$f=\frac{1}{\sqrt{(x_p-x_{p0})^2+(y_p-y_{p0})^2+(z_p-z_{p0})^2}}$$ I need to integrate this function over the cylindrical surface $S_1$ containing point $(x_{p0},y_{p0},z_{p0})...
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0answers
41 views

How can I get a symbolic result for the following integral?

I have the following integral which I would like to solve analytically, if possible $$\frac{1}{T} \int_{0}^{T} \frac{\left( x^{2} - (x_{0} + e^{-t})^{2} \right)^{2}}{\left( (x_{0} + e^{-t})^{2} ...
0
votes
3answers
54 views

Graphing and arch length of a cycloid on Mathematica

Graph the cycloid $x=t- \sin t$, $y=1- \cos t$ and find the arc length of one arch of the cycloid.
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1answer
75 views

Mathematica crashes after symbolic integration

I have a very serious problem. I want to integrate the function func symbolically. I've checked the result numerical which agrees with literature but I need the analytical expression of the computed ...
-1
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2answers
46 views

Line Integral with Vector Plot Parametric Plot and Show

How can I make different plottings of this line integral where $C$ is the square bounded by lines $x = \pm 1$ and $y = \pm 1$. $$ \begin{equation} \int_C 4y^3dx-2x^2dy \end{equation} $...
0
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1answer
70 views

How Mathematica handles Heaviside functions?

I have a question on how mathematica computes this simple example. I can't reproduce this result on paper: ...
0
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0answers
32 views

Correct use of differentiation

I have a PDE of the form f = F[x,y,z,u,ux,uy,ux] where u = U[x,y,z], ux = D[u,x], uy = D[u,y], uz = D[u,z]. If I want to ...
0
votes
2answers
66 views

Positiveness of two variable inequality

How to show that the function g[a_, n_] = -4 a^2 + 8 a^3 - 4 a^4 + 16 a n - 24 a^2 n + 8 a^3 n - 12 n^2 - 4 a n^2 + 12 a^2 n^2 + 12 n^3 - 8 a n^3 of ...
0
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0answers
55 views

Infinitesimals in Mathematica

Is it possible to parse for Mathematica the following function ? f[x_] := x + t, Where t is infinitesimal $dx$ ? I work on ...
0
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1answer
48 views

Using subscripted symbol affects integration — why?

Below is a sample program that shows that Integrate is giving different results depending on whether I name the variable duration1 or ...
0
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1answer
37 views

Why do Integrate and DSolve/DSolveValue yield such complex expressions for Piecewise functions?

This code uses two different methods for integrating a very simple piecewise function but yields surprisingly complicated integrals: ...

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