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.
5,049
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Derivative at the point
How can I get a derivate at the point? I've specifyed a boundary condition for my PDE:
lb = - c D[u[x, t], x][a, t] + d u[a, t] == gamma
When I present the ...
1
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0
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1k
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Invalid integration variable or limit(s), for a complex function
I am a beginner in Mathematica. I'm wondering if Mathematica could do the integration of a complex function and plot the values in a 3D graph.
Here is the code.
...
2
votes
2
answers
106
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Triple integral with exponentiation
I would like to integrate
Integrate[x*E^(x^2 + y^2 + z^2) Boole[x^2 + y^2 + z^2 <= 1], {x,0,1}, {y,0,1}, {z,0,1}]
However Mathematica gives me
...
5
votes
1
answer
262
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Why do I get quadrature points $\notin [0,\infty]$, when making own Gaussian quadrature rule with range $[0,\infty]$?
For my project, I'm trying to calculate in Mathematica my own Gaussian quadrature rule (i.e. the quadrature points and weights) for a certain model with a parameter $x$ with the following (Maxwallian) ...
12
votes
1
answer
390
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Getting wrong limit with Bessel
Bug introduced in 7.0 or earlier and fixed in 11.3
I computed a following limit (related to the asymptotic expansion of the sequence A000009 - number of partitions ...
1
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1
answer
553
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integral over a region boundary
I want to integrate a complex function over a boundary of a region:
$$-\frac{i}{v}\oint_\Gamma \exp(-2\pi i(ux+vy))\,dx,$$
where $\Gamma$ is the closed boundary of a region and $y = f(x)$.
I know ...
1
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0
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67
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Different Derivative's output with ComplexExpand
Consider this expression
f = Abs[ x + I ]
with this assumption
$Assumptions = Element[x, Reals]
Now there is something ...
-2
votes
2
answers
100
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Integrate fails while NIntegrate works
I'm having an odd issue where I am integrating a function (f) (a summation of Legendre polynomials so a polynomial of large order) on a finite domain where the ...
0
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1
answer
67
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Writing a program that can verify the color of a plot asked to a user
I hope this title isn't misleading, but I am creating 2 programs that ask a user a series of questions in regards to derivatives and plots and I will explain as thorough as possible. I don't have a ...
1
vote
1
answer
64
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Differentiate an Integral-Assumption needed
I already looked into the smaller problems, but I just don't get the clean first derivative, because Mathematica wants to work with imaginary numbers. How do I best supress this here? I tried it with <...
0
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1
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512
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Variable integration limits over real numbers only [closed]
I have a simple question regarding this code:
...
-1
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1
answer
88
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Calculating exponential Integrating
I tried to find the answer for below integration in Mathematica but I got no response. Could anyone help me?
Integrate[E^(a Cos[x - x0]), x]
1
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1
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145
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Why can't Mathematica evaluate this limit of 2F1, which actually is a polynomial?
Consider the following function:
test = (1 - q) Hypergeometric2F1[-(1 + q)/2, 2, 1 - q, x];
It's quite obvious from the definition of $_2F_1$ that the above ...
1
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1
answer
217
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FourierTransform breaks function symmetry
The fourier transform of a seemingly simple function gives me a complicated result: (I imaginary unit)
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6
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3
answers
1k
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Can Mathematica automatically calculate and sum over residues at all poles of a (rational) function?
The title basically says it all: is there a way in Mathematica to automatically compute the residues at all poles of a function $f(z)$ and present them as well as their sum in a list or table?
A ...
0
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1
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515
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How to involve a variable in numerical integration? [duplicate]
Now I have two functions f[x] and g[x] which both contains another variable a, or we can note as f[a,x] and g[a,x]. Now I need to solve the equation
...
1
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1
answer
221
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Help Evaluating Infinite Definite Integral
I am reading a publication and trying to follow all of the derivations, but I am having trouble evaluating the following integral which they say has a solution!
...
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2
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180
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How to get the numerator of this fraction involving `Csc` or `Sec`?
I would like to avoid multiplying explicitely by the denominator, because I'm working with huge fractions.
Consider
...
0
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1
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108
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Plotting two integrals [closed]
I am having troubles in trying to plot those two integral functions:
$$\text{Ei}(z) = -\int_{-\infty}^z \frac{e^t}{t}\ \text{d}t$$
$$\mathcal{E}_1(z) = \int_z^{+\infty} \frac{e^{-t}}{t}\ \text{d}t$$
...
5
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4
answers
449
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`Series` with non-analytic terms
I have a function which has a smooth non-analytic term, a simplified version of which is
$$
f(\lambda) = \frac{1}{1 + k \lambda + e^{-1/\lambda}}.
$$
I want a series expansion of this, in Mathematica, ...
0
votes
1
answer
59
views
Computing a limit symbollically, it is possible?
I want to compute this limit symbollically
Limit[Abs[1 - a^k]^(1/k), k -> Infinity]
but it does nothing. I tried defining a...
2
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1
answer
523
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There is a way to evaluate the limit superior of a sequence?
Is there a way to evaluate the limit superior of a sequence?
I didn't find any information about this in the documentation center.
The limit superior of a sequence $(x_n)$ is defined as
$$\limsup ...
0
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0
answers
72
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Same expression but different derivatives
Consider this expression
VexpansRI = Conjugate[ A + (I dI + dR + vd/Sqrt[2]) (I sI + sR + vs/Sqrt[2]) (I uI + uR + vu/Sqrt[2])]
Now since
...
2
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1
answer
496
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ReplaceAll does not work on derivatives
(q''[x] - Exp[q[x]/2)] /. q[x] -> y[x] + a*t[x]
gives
-Exp^[1/2 (y[x] + a*t[x])] + q''[x]
Which is not what I want.
I ...
0
votes
1
answer
507
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How to solve and plot Definite Integral with Symbolic Limits
I need to plot g1, g2, g3 and g4 expressions. To do that, I am trying to evaluate the double defined integral in the three expressions, however I am having issues because one of the integration limits ...
3
votes
1
answer
314
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How do I quickly estimate the area under a complex curve?
I have written a Manipulate function that shows the changing photoperiod (number of hours of daylight per 24-hour day) to which a latitudinal migrant is exposed before, during, and after each of its ...
1
vote
0
answers
35
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Defining a differential for use in a later differentiation [closed]
Suppose I have some function that I want to differentiate e.g. $f(t) = x(t)y(t)$.
I can do this in Mathematica as,
D[x*y, t, NonConstants -> {x, y}]
to ...
4
votes
3
answers
152
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limit of a radical
I want to find the limit of infinite nested radical, but I don't know how to express this in mathematica. I used Fold[] but I couldn't make it exactly like this.
12
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1
answer
1k
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How to do a line integral visually in version 10 or later
In version 10, Mathematica introduces some Region functions, which allow us to do integrals very visually. We can do this even if we don't know any Mathematica syntax and it can help me show others ...
3
votes
2
answers
9k
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The partial derivative symbol with subscript - what does it mean and how do I type it?
The guide that I am using to study Mathematica tells me to type the following
to get
I am stuck at the partial derivative symbol because I do not understand what it exactly means with the ...
0
votes
1
answer
125
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Mathematica returns unsolved integral [duplicate]
I have the following integral:
...
0
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1
answer
82
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Compute derivative of a composed function leaving indicated some derivatives [closed]
Is there a way to define in Mathematica a generic differentiable function $g:\mathbb{R}^2\rightarrow \mathbb{R}$ in such a way that when it computes the derivatives of a composed function involving $g$...
0
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0
answers
260
views
Separation of variables in partial differential equation
I have a differential equation which possibly depends on all independent variables of the problem
...
-2
votes
1
answer
299
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numerical differentiation [closed]
I have a function f(z,x),but it is a list of data. It is also in two variables z and x that are lists of data too.
I need to find gradient f(z,x). In another word, how I find a numerical ...
3
votes
1
answer
168
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Derivative ParametricNDSolveValue
i'm work with heat conduction in cylindrical coordinates, my problem is how to calculate a derivative for a parameter using ParametricNDSolveSolution.
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1
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70
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Derivative of MeijerG function wrt to one of its parameters
I would like to evaluate numerically the following expression
$$
\left.\left[\dfrac{\partial}{\partial b}G_{2,4}^{4,0}\left(2\left|\begin{smallmatrix}0&\tfrac{1}{2}\\b&b&b&b\end{...
1
vote
1
answer
487
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Laurent series 0 < |z-3| < 3
I wanna check my laurent series exercises on Mathematica, but can't seem to find a command or program to achieve the result of such type of interval.
$f(z)=\frac{1}{(z-3) z},\\1<|z-3|<3$
The ...
0
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1
answer
148
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Numerical evaluation of derivatives [closed]
I have a function defined as
L[t_] := exp[-0.9239*t]*(0.2310 cos[0.3827*t] + 0.0957*sin[0.3827*t]) + exp[-0.3827*t]*(0.0957 cos[0.9239*t] + 0.2310*sin[0.9239*t]);
...
1
vote
1
answer
397
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show detail steps of an Integration [duplicate]
I compared the results of an integration exercise, one was done by Mathematica Alpha, the other one was done by hand on my own. I'm sure MA is right, however I could not find out which step went wrong ...
0
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1
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119
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Why Mathematica is incapable doing fast symbolic integrations
I need to calculate this symbolic integration below, but kernel has still been running for a long time and it has not come up with a solution yet. Could you have a look at it, I was wondering if there ...
3
votes
2
answers
571
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Automatic simplification of trigonometric functions with negative arguments [closed]
I'm fairly new to mathematica and its ability to define pure functions. I was using it to work on a school problem. The idea was to derive a vector with two trig functions that I could set another ...
0
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2
answers
91
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How big of an integer does k have to be so that the slope of f(x) at Sqrt[k] is greater than 20?
Here is my function:
f[x_] := x^2 + k*x
I can plot this function to see its behavior but I certainly cannot obtain an answer by this visualization
...
2
votes
3
answers
353
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Incorrect Result for Multivariable Limit $\lim\limits_{(x,y)\to(0,0)}\frac{2x+y} {x+3y}$
Edit
I just realized that I don't have to worry about this; the worksheet says "Find the value of the limit using Mathematica or justify the limit does not exist". I've already done so by hand, so me ...
5
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2
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3k
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How to make a matrix of derivatives? [duplicate]
For example I can construct:
row1 = D[f(x,y),x,#]&/@{x,y}
row2 = D[f(x,y),x,#]&/@{x,y}
then:
...
1
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1
answer
100
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Challenging antiderivative loop
I am attempting to create a loop (either Do, For or While) that will continue to take antiderivatives of f(x)= x until the area under it between 0 and 10 is greater than 1000. And whichever function ...
3
votes
1
answer
279
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Writing a loop for multiple derivatives along with roots for each derivative
I am trying to write a loop that will take the first n derivatives (lets say n =3), which outputs a list that will include 1(or more) roots for each derivative.
I haven't actually set up the loop ...
0
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3
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811
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Specifying multiple assumptions in the integration
I have to calculate following integral
$$ \int_{-\infty}^{\infty} \frac{d \omega}{(i \omega +(\mathbf{k}-\mathbf{p}).(\mathbf{k}-\mathbf{p}) ) (-i \omega + (\mathbf{k}+\mathbf{p}).(\mathbf{k}+\mathbf{...
2
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0
answers
160
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Simplifying expressions containing derivatives of the assumptions
I want to Simplify expressions with terms like these:
D[f[x,y],x]-D[g[x,y],x]+...
but when i use
...
1
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2
answers
138
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Passing a function and its derivative to a module
This is a classical way to calculate Lyapunov exponent
...
0
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1
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77
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Defining a derivative as a function [duplicate]
I'm trying to define the following function
Df[k_, t_, x_, M_] = 1/Factorial[k] D[Exp[-(4 M x t)/(1 - t)], {t, k}]
I want to differentiate that exponential with ...