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.
5,409 questions
0
votes
0
answers
112
views
Different versions of Mathematica generate different results
I am trying the following integral and different answers from Mathematica using two different versions. Please compare the last terms. Which one should be trusted. Please see below:
Input:
...
- 669
3
votes
1
answer
160
views
Why the difference in the results of Integrate and ContourIntegrate?
In 14.3 on Windows and Wolfram Cloud the results of the commands
ContourIntegrate[Exp[I*x]/(x^2 - 2*I*x - 2), x \[Element] InfiniteLine[{{-1, 0}, {1, 0}}]]
...
- 30.4k
2
votes
1
answer
148
views
How to avoid complex numbers in these integrations?
In 14.3 on Windows and Wolfram Cloud the command
Integrate[Sqrt[1 + Tan[x]], x]
produces the result with the imaginary unit
...
- 30.4k
8
votes
2
answers
333
views
Mysterious second argument of DifferentialRoot
In the documentation of DifferentialRoot, there is a rather mysterious remark (last item):
DifferentialRoot[lde,pred] represents a solution restricted to avoid
...
- 391
7
votes
3
answers
422
views
How to obtain this asymptotic of the sum of the series?
The results of the commands in 14.3 on Windows
AsymptoticSum[(-1)^(k - 1)/k, {k, 1, n}, {n, Infinity, 1}]
...
- 30.4k
0
votes
0
answers
89
views
Avoiding higher order terms from Integrate output
I want to integrate the following expression and obtain a result where there are no second order terms. My motivation is to use Mathematica to derive the weak form of PDEs in a systematic way. ...
- 459
0
votes
0
answers
100
views
Residue of a complex integrand with trigonometric terms and exponential factor
UPDATE
I am trying to compute the residue of the following integrand arising from a contour integral:
\begin{equation}
-\frac{1}{2\pi}\int_{C^{+}} \frac{1}{\tilde{\Delta}(\lambda)} \
\Bigg\{2 i \...
6
votes
2
answers
540
views
Integration result without using Rubi
I am looking at this Mathematics SE integral and am wondering if there is a way to get the result without using Rubi (I am not sure if it can do it either)?
...
- 3,648
3
votes
1
answer
173
views
How to plot the numerical integral solution with respect to input variable?
I have the following integral
$$\int_{1}^{x} \left(3x +5 \right) \, dx = 2 t $$
I want to numerically plot an integral solution of x as function of t or x(t) versus t without going into analytical ...
- 925
2
votes
2
answers
275
views
Definite Integral of square root of a quadratic function
when I find the following integrals, I get complex solution inspite of the fact everything is real and argument of the square root is always positive.
...
- 669
9
votes
4
answers
482
views
Approximating Bessel $K_0$
I often face a problem that some special functions are not readily available in common programming languages (e.g. Fortran) without using specialised libraries. Therefore I want to be able to quickly ...
- 25k
4
votes
1
answer
187
views
Integration over the same ball specified in different ways gives different results
I tried to calculate the electric field intensity of a uniformly charged sphere, both inside and outside, using a triple integral whose integration region was specified in various ways. The following ...
- 561
2
votes
2
answers
428
views
Why won't Wolfram Engine perform this integration?
I want to find the exact value of this definite integral in terms of c and q with the following assumptions:
...
- 406
1
vote
0
answers
87
views
Is there any way to get an exact solution for this integral of a piecewise function that has singularities?
I want to find the exact (not approximate) value of a definite double-integral involving a complicated piecewise-defined two-variable function p[Theta, Phi] (whose ...
- 406
4
votes
0
answers
270
views
How to convert PDE into ODE?
I have a function J(x,y) = J(y,x) which satisfies the following PDEs with $\theta_x = x \frac{\partial}{\partial x}$ and $\theta_x = y \frac{\partial}{\partial y}$
$(1+\theta_x) (1+\theta_x+\theta_y)(...
- 1,170