# 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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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 ...
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### 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 ...
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 ...
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### 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 ...
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### 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 ...
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 ...
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 ...
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### 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: ...
48 views

### Should I believe this numerical trivariate integration result involving Liouville's constant to fifteen decimal places?

I have two constraints ...
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,...
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 ...
67 views

### Jacobian of Mod function giving zeros as result

Could you please explain the following discrepancy in results ? ...
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 ...
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])^2 + (D[r])^2] How do I properly reference a single ...
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### 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 ...
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: ...
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### 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 ...
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 ...
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### 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:...
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 ...
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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: ...
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 ...
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 ...
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 ...