# 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 ...
1 vote
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 ...
205 views

### Finite Differences:

I am having difficulty implementing finite differences in the correct columns of my code. ...
67 views

### Integral of interpolation function is not evaluated

I am having a misunderstanding with Mathematica about integration of InterpolatingFunction. Consider this example: ...
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### 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 ...
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### 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....
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### 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....
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### 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 ...
1 vote
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: ...
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### 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[]] ...
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