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.
4,199
questions
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Reduce or Limit to have positive value!
I would like to see where this function is positive ??!!
Reduce[{Tanh[x]/Sqrt[-1 + Tanh[x]^2] > 0}, x, Reals]
thank you.
2
votes
1
answer
81
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Plotting, Integrating two variable function with cross-restricted domain
Hello, I have two problems.
the first is plotting 3D function, the domain is "0<x<y<1". (I could find examples like integrating function with domain 0<x<1, 0<y<1, but I ...
- 135
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vote
1
answer
123
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Integral of orthogonal Bessel functions
This is the basic form of the problem i am solving.
The main difference with the integral on the photo and my example is that i have my integral defined from b to c instead of 0 to a, and Bessel ...
- 65
0
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0
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48
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Integral with triangular functions in exponential and numerator
I am trying to find the solution of an integral with a triangular function in the numerator and in an exponential, but after an hour Mathematica has not given me an answer. I wondered if there is a ...
- 131
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53
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Useless and incorrect result of AsymptoticIntegrate
In version 13 on Windows 10 I try to find asymptotic of the integral used in potential theory
...
- 16.8k
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0
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41
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Output of expressions unable to have operations be performed on the expression
I am currently trying to use the code linked in the catalog of spacetimes pdf to calculate chirstoffel symbols for a metric which follows as
n := 4
...
- 119
0
votes
1
answer
46
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Plot for DSolve in mathematica [closed]
I don't Plot it's not working!!, can you help me?
...
2
votes
1
answer
51
views
Integration over an implicit region
A question asks me to calculate the following integral using NIntegrate:
Calculate the double integral ... where D is the area bounded by the four lines ...
With ...
7
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3
answers
1k
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Mathematica 13.0 simplifies trigonometric integral wrong
I calculate the following general expression:
...
- 73
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0
answers
59
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Getting a wrong plot after NIntegration
I am trying to plot this function numerically.
R2T = ...
1
vote
1
answer
29
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Getting the same result from Integrate as Probability
I'm trying to solve a Baysian inference problem (although the details are not all that important for this question)
I define two probability distributions P and <...
- 819
0
votes
1
answer
61
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Numerical Plot for an example
I would like to compare the numerical and analytical solution with plot for this example but something is wrong I don't know how to fix it?!!
...
- 381
1
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0
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66
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What's the meaning of Global?
I'm calculating an integral,
Integrate[(t e^(-z t) e^(-q t))/(1-e^(-t)), t],
and the result is
...
- 121
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0
answers
54
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Settings that integrate gives also distributions as solutions
How can I tell Mathematica that I also want distributions as solutions for Integrate?
Example:
$$\int_{\mathbb{R}} \mathrm{e}^{\mathrm{i}kx}\mathrm{d}x=2\pi\delta(x)$$
- 101
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votes
0
answers
39
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Replace Derivative[ i ][ f ][ t ] with f[ i, t]
Assume the PadeApproximant is carried over f[t0] * g[t0] with the order {1, 1}, that is
<...
0
votes
2
answers
101
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Integrate: slow and wrong results
Very often I struggle to understand what is happening when I try to integrate stuff in Mathematica. Generally, it deals very well with ugly symbolic integrals. But I have an example in which it deals ...
- 169
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2
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68
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0
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0
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58
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DSolve doesn't solve a second order differential equation
I am trying to solve an ordinary differential equation:
...
10
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3
answers
2k
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Can Mathematica calculate this elliptic, triple integral?
Integrate[(4 a b/Pi) (a^2 + b^2 - 2 a b Cos[c])^(1/2), {a, 0, 1}, {b,
0, 1}, {c, 0, Pi}]
I'm using basic plan, it gives me the result like that.
The ...
- 135
-3
votes
1
answer
70
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Taking sentences with a spatial factor [closed]
To ask my question precisely, I should say that I have got many terms, among them some have coefficients $M^n$. Some things like :
$$f = f_1(M) + f_2(M) + M f_3(M)+ M^2 f_4(M)+f_5(M)+...$$. I need to ...
- 57
0
votes
1
answer
74
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How come I can't get $\int f(t)$ from performing derivative/anti-derivative operation on $\int f(t)$?
I know the the area under the curve of some function between the coordinates $t_0$ and $t_1$, is:
$$\int_{t_0}^{t_1} f(t) \space dt=\frac{\left(t_0^2+t_1^2\right)^2}{4t_1^2}$$
How do I find $f(t)$?
I ...
- 1,481
2
votes
1
answer
69
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Selecting a solution range that is independent of a variable value
This symbolic computational question derives from this mathematical one on math.SE:
Find all values of $a \in \mathbb{R}$ for which $f(x;a) = x^3 - 3 a x^2 + 3 a x - 2$ is non-decreasing.
My ...
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2
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1
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118
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How to integrate this product of Exp[] and Cos[] using Mathematica
I would like to integrate the following product of Exp and Cos：
...
- 699
5
votes
1
answer
109
views
Evaluating PlusMinus to 2 decimal answers
How do I evaluate and expand an expression containing PlusMinus such that:
N[PlusMinus[1, 1]]
returns
2, 0
I'm stuck at ...
2
votes
0
answers
43
views
Why does Mathematica not know some integrals diverge?
I want to analyse the convergence of some complicated 1d integrals that may have divergences at $x=0$, similarly to the harmonic integral $\int_0^a 1/x \ \mathbb{d} x$, which I know is divergent.
When ...
- 21
0
votes
2
answers
36
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`Assuming` combined with mathematical notation of `Integrate`
I am trying to write down the following expression
Integrate[Exp[-a/2/x]/x/(x + 1), {x, 0, b}, Assumptions -> a > 0 && b > 0]
using mathematical ...
- 1
0
votes
1
answer
68
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The inverse Laplace transform alters parameter constraints
I have this Laplace transform:
$$\left( w \frac{L}{L+s}+(1-w) \frac{Q}{Q+s}\right)^n \ for \ L>0, Q>0,0<w<1.\ (1)$$
...
- 187
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0
answers
50
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splitting integrand based on variable dependence
For multiple integration, I would like to automatically check whether the integrand can be split up to a product of terms, each dependent on as small a subset of the variables as possible.
E.g., given ...
- 917
0
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0
answers
33
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Integer parameter assumption gives incorrect result when integrating
There are some dangerous pitfalls that can happen when evaluating some integrals, assuming that some parameters are integers. For example, consider the following:
...
- 951
0
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0
answers
45
views
Algorithm: Permutations & Signature
Theoretical side
Simple example: If I have two sets $A_1=\{1,3\} ,A_2=\{2,3\}$
and Permutations[{1, 2, 3}]= $\left(
\begin{array}{ccc}
1 & 2 & 3 \\
1 &...
- 574
1
vote
1
answer
61
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How to perform the first and second derivatives of Nth polynomials?
Suppose
$P(x,y)=\displaystyle\sum^{N}_{i+j=0}\alpha_{ij}x^{i}y^{i} \equiv \alpha_{00}+\alpha_{10}x+\alpha_{01}y+a_{11}xy+\ldots+a_{0N}y^{N}$
is a multivariable polynomial of $N$th degree. I want to ...
3
votes
1
answer
102
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Inconsistent results between NIntegrate and Integrate
I get these inconsistent results
What is going wrong? Fast oscillating terms? Small exponential factors?
But then, why the result seems to toggle between values 1 and 2, rather than being a real ...
- 315
0
votes
2
answers
44
views
Limit is not actually evaluated, but wolframalpha does [closed]
I'm trying to evaluate the limit $\lim_{x \to a} f(x)$ of the function $f(x)=\dfrac{1}{1+\tfrac{a^2}{4x(a-x)}\sin^2 \left(b\sqrt{a-x} \right)}$ using mathematica, and it should yield $\dfrac{1}{1+ab^...
1
vote
1
answer
69
views
How do we just have $\log$ solution?
Mathematica solves this but I want the solution just as Ln[..]?!!
DSolve[y'[t] == 3/2 a*y[t] ((y[t] + b)^2 - f), y[t], t]
thanks
0
votes
0
answers
107
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Dictate Mathematica to use the contour integration method
I want to evaluate an integral, which can be in principle computed exactly. For $a>0$ and $k_1, k_2 >0$, define $G(x) = (x+ia)^3$. The integral that I have is
$$I = \int_{\mathbb R^4} dy_1dy_2 ...
- 909
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0
answers
39
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How to analytically solve for an intersection of two functions on an interval?
I would like to analytically solve for the intersection of two functions on a given interval and store the solution as a function (of parameters) for later use. How can I tell Mathematica to look for ...
- 77
1
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0
answers
23
views
Commutation of the partial derivatives on scalar in xAct
I do not know how to automatically commute partial derivatives on a scalar and simplify it. For example, if I have:
$$\partial_a \partial_b \partial_c f- \partial_c \partial_a \partial_b f $$ where $f$...
- 57
4
votes
2
answers
149
views
The jumping problem when rolling reuleaux triangle
I'm making an animation of a Reuleaux triangle rolling on a straight line like this
The animation generated by my code is not continuous, is there a simple way to eliminate jumping?
...
- 4,910
0
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1
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74
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How to get the derivative from this implicit equation with differentials? [duplicate]
The idea is here to have a implicit equation and take from both sides of the equation the differential and solve out of this the derivative
The derivative is the ratio of two differentials and can be ...
- 649
0
votes
2
answers
77
views
How to set integral starting from 0 in the symbolic solution to ODE
I have the following ODE
Bfull'[t] == - (p0/(
p0 + (1 - p0) E^Integrate[α[s], {s, 0, t}])) * α[
t] (S[t] - Bfull[t]) + α[t]*c + δ * Bfull[t]
where α and S ...
- 53
2
votes
2
answers
108
views
Plot the general and a particular solution for this differential equation
In a previous question, I had obtained a differential equation from:
Starts with this implicit equation:
(x - a)^2 + y^2 == 1(1) ( circles on x -axis ) $(x-a)^2+y^2=...
- 649
2
votes
1
answer
94
views
How Implicit differentiate in order to get a differential equation [closed]
Starts with this implicit equation:
(x - a)^2 + y^2 == 1(1) ( circles on x -axis ) $(x-a)^2+y^2=1$
Is the set of equations of the given circles. This set contains ...
- 649
5
votes
1
answer
247
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Poincare section for a perturbed string
I am trying to find the Poincare section of a perturbed string in a gravitational background with a magnetic field. The plots that I am trying to reproduce are from this paper (page 11).
The code that ...
- 181
1
vote
1
answer
103
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Integrals on symbolic regions
Let's define a region as r=Polygon[{{-a,0},{a,0},{a,h}}]. I want to integrate some function over that area. Say x^2. So, ...
- 708
1
vote
1
answer
61
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Solve functional integral equations
I encountered one problem which is to find $F(\lambda)$ which satisfies
$1 = \int_{-\pi}^\pi e^{i k \lambda} dF(\lambda), \forall k \in \mathbb{Z}$ and the answer is $F(\lambda) = 1$ if $\lambda \ge 0$...
- 13
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2
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81
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6
votes
3
answers
314
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Neglecting higher order terms in a Lagrangian
I have a lagrangian which is modified by variable change. I want to neglect all the 4th order and higher terms in the new lagrangian. The code being used is given below:
...
- 181
0
votes
2
answers
77
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Assumptions in Integration for positive real values [closed]
I want to evaluate the following integral in Mathematica.
$$ \int_0^\infty \frac{a^{-t}-b^{-t}}{t} dt = \ln \left(\frac{\ln b}{\ln a} \right)$$
I try to enter this, but Mathematica can't figure it out....
- 1
0
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1
answer
66
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Power Series and Interval of Convergence [closed]
How could I find the power series and interval of convergence for x/(3+x^2)?
- 1
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3
answers
244
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Computing the elliptic integral $\int \frac{1}{x \sqrt{f+\frac{a}{x^3}-\frac{k}{x^2}}} \, dx$
I don't know how to solve this with or without Rubi?!!
...
- 381