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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1answer
384 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
3
votes
0answers
26 views

Differentiation and series expansion of dot product - inconsistent results

If I differentiate a dot product, I get the result I expect D[a.b[x], x] (* a.b'[x] *) However, a series expansion of the same expression gives a very different ...
0
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0answers
29 views

Coordinate transformation for gradients expressions

Let's suppose I have an expression in cartesian coordinates, involving gradients, such as: F[x,y]:=D[f[x,y],x]/D[f[x,y],y]+D[f[x,y],y,y] f[x,y] Now, I would like ...
4
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0answers
174 views

Version 8.0 integrates but Version 9.0.1 doesn't

I am trying to run the following integral in version 9.0, but it fails: ...
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0answers
22 views

Trouble evaluating an integral for certain parameters [on hold]

I'm trying to evaluate the integral $$ \int_0^{2\pi}\pi(2(\Delta x-d+r'e^{ix})I_o(rd) - \sqrt{2b(b-\sqrt{b^2-1})-1}(e^{-b/2(r^2+4r'^2+8(\Delta x - d)r'cos(x))-2i\sqrt{b^2-1}drsin(x)}dx $$ using <...
1
vote
1answer
95 views

Computing integrals in Mathematica

I am trying to actually compute $\int \sqrt{\cosh{y}-\cos{x}}e^{inx} dx$ in mathematica. As an example i tried computing $\int \sqrt{1-\cos{x}}e^{inx} dx$ and got a result. But when i try $\int \...
0
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1answer
48 views

Can this expression be calculated symbolically?

I want to do definite integration of the following expression ...
0
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0answers
66 views

How to compute this integration? [on hold]

I would like to compute the following integral: I tried to write it as ...
1
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1answer
79 views

integrating with multiple indicator functions depending on each other

I need to compute the following integral with three indicator functions, $I(x)$, $I_1(x_1)$ and $I_2(x_2)$, $$ \int_0^1\int_0^1I(x)\left( \ I_1(x_1)\,x_{1} + I_2(x_2)\,x_{2}-1 \right) dx_1 dx_2 $$ ...
1
vote
1answer
67 views

Evaluating Bessel-Schläfli-type Integral with Infinite contour

I am attempting to evaluate the integral \begin{equation} \int_{\infty-i\pi}^{\infty+i\pi} dt \frac{e^{-\frac{l}{n}t}}{[(X'-X)^2+r^2+s^2- 2rs \cosh(t)]}, \end{equation} the only variable being $t$, ...
2
votes
2answers
117 views

Symbolic linear algebra gradients/matrix calculus

Can Mathematica generate symbolic expressions for gradients? For example, if $x_1$ and $x_2$ are two points, could I get Mathematica to generate expressions similar to the following? $\frac{\partial ...
0
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0answers
50 views

Doing vector calculus with element-wise defined formulas and arbitrary-sized vectors [duplicate]

Currently I am trying to make Mathematica handle vector expressions defined element-wise. For example, But I can find no way to do this. Every way I tried requires a fixed-sized vector and returns ...
3
votes
2answers
134 views

Symbolic Integrate fails after almost 1 hr calculation

Mathematica 9. I want this Integrate[( Cos[t ω]^2 Cos[α + t ω])/(-1 + A Cos[α + t ω])^2, {t, 0, (2 π)/ω}] Can Mathematica handle with it? I tied different ...
2
votes
3answers
128 views

NDSolve and differentiation of Abs

I have found several questions about the derivative of Abs and how it is not defined in the complex plane. What I have not found yet is a precise and simple ...
1
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1answer
125 views

Residue failed to reproduce this residue in a paper

This problem is a more clearly state of my original problem which is off topic, so I reconsider my problem carefully based on previous discussions, and gives the following valid code to reproduce my ...
0
votes
1answer
45 views

How should I compute this triple integral? [closed]

I have tried taking the triple integral of $x \cos(y)$ with the bounds $0<z<1-y, x^2<y<1, -1<x<1$ in the order dz, ...
1
vote
3answers
128 views

How to calculate the double integral of a double integral?

May I ask is there any wise way to calculate the following integration? $\int_{-1}^{1}\int_{-1}^{1}\int_{-1}^{1}\int_{-1}^{1}\frac{\left( 0.25 \left(-1+\eta _1\right) \eta _1 \left(-1+2 \eta _2\right)...
0
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1answer
56 views

Integral of $(\sin x)^3(\cos x)^3$ [closed]

For the integral of (sin x)^3(cos x)^3 I got 1/6(cos x)^6 - 1/4(cos x)^4 + C. This seemed to work but my book had 1/4(sin x)^4 - 1/6(sin x)^6 + C. This is similar to what I got but instead of cosine ...
2
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0answers
61 views

Why does Expectation function compute, while explicit integration does not?

The code: Expectation[1 + 1/y, {y \[Distributed] ExponentialDistribution[1]}] outputs 1 - EulerGamma While, ...
0
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0answers
59 views

Are the following implemented: Differentiable, Continuous, Interior Point? [closed]

FunctionDomain is a great Mathematica function. It tells you the natural domain of an expression. Has anyone (or is anyone) working on a similar thing for checking ...
1
vote
2answers
132 views

How to convolve the unit box function and the modified Bessel function of the second kind in 2D?

In 1D the convolution of the unit box function and the modified Bessel function of the second kind $K_0(x)$ works very well. ...
0
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0answers
42 views

How can I evaluate a line integral? [closed]

Can I compute a line integral with Mathematica? I have tried entering the t values into my expression, but I am not getting an answer. For example: ...
1
vote
2answers
217 views

How to find a graphical solution for extreme values using Lagrange multipliers

I need to find the maxima and minima of a function. I managed this analytically with no problem, but now I need to show in a graphic the intersection of the functions. My function is: ...
11
votes
6answers
876 views

Integrate gives wrong results

Integrate[a/(Sin[t]^2 + a^2), {t, 0, 2 Pi}] $$\int_0^{2 \pi } \frac{a}{a^2+\sin ^2(t)} \, dt$$ gives $0$ This cannot be true. What is going on? If I insert a ...
7
votes
3answers
635 views

Any way I can evaluate this integral?

So, Mathematica can't evaluate it. Any workaround? $$\int_0^\pi \frac{\mathrm{d}\theta}{\sin\left(\frac{\theta}{2}\right)^\beta + 1}$$ The code is: ...
1
vote
1answer
103 views

Evaluate an integral with parameters

I already asked this on stack overflow but was redirected here. I am trying to solve the (highly non-linear) following system of equations : with and $g_0$, $\Lambda$ are positive constants ...
1
vote
1answer
66 views

Problem in limit of exponential function

I want to obtain Exp[-α/(1 - α)] /. {α -> 1} The output is Indeterminate. But I calculate without Mathematica and I ...
1
vote
1answer
64 views

Need help on simplifying the integral of a square root of a polynomial

I have the following expression a = 4 Cos[af / 2]^2; b = 1 - 5 Cos[af / 2]^2; c = Cos[af / 2]^2; s = Sqrt[a*x^4 + b*x^2 + c] and I need the integration of $s$ in ...
2
votes
2answers
97 views

Analytic differential of an inverse transcendental function

I have the following function: $$ y(x)=\frac{Ax}{Bx^{1/4}\sinh{(\frac{Bx^{1/4}}{2})}}\left(\cosh{(\frac{Bx^{1/4}}{2})}-1 \right), $$ where $A=112.941$ and $B=18.6588$. I want to find the differential ...
3
votes
1answer
98 views

Using Vector Operations In Mathematica

I would like to calculate $$ \mathbf T = (\mathbf B \bullet \nabla) \mathbf B$$ Where nabla (the upside down triangle) is the grad operator $(\partial/\partial x,\partial/\partial y,\partial/\...
0
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1answer
130 views

Integrating SquareWave - don't understand result

Integrate[SquareWave[t], t] // InputForm Gives as output Piecewise[{{-t, Inequality[1/2, LessEqual, Mod[t, 1], Less, 1]}}, t] ...
8
votes
2answers
155 views

Integrate and NIntegrate disagreeing over branch cut of Sqrt?

Bug introduced after v8.0.4 and before v9.0.1, and persisting through v10.4.1. In Mathematica 10.2 I'm trying to integrate this piecewise continuous function, but ...
3
votes
2answers
137 views

Integrate on a contour in the complex plane

I want to integrate the function f[z]= z + Conjugate[z] over a circle of radius 2 centered at the origin. For the sake of stating something that I have tried: <...
0
votes
1answer
83 views

Definite and indefinite integral give different results

I'm trying to find an expression that, given $x$, $y$, and $R$, gives the indefinite 2D integral of a function at the circle centered on $(x_0, y_0)$ with radius $R$. With $g$ as defined below, I'd ...
0
votes
2answers
92 views
3
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2answers
86 views

Application of # for the $n^{th}$ derivative

Let's say that I have x^2+x Is there a way to map $x$ to the first derivative of a function and $x^2$ to the second derivative of the same function? According to ...
0
votes
0answers
10 views

Trying to find integral of square root function. [migrated]

I am trying to find the integral of x sqrt(36-6 x^2) with a = 0, b = sqrt(6) When I use the substitution rule, I get u = 36-6x^2, which results in an imaginary number: 1/12(u^(3/2)) du My textbook ...
10
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1answer
103 views

Slot number cannot be filled

I got a strange message with the derivative of a two-argument function defined by a definite integral. For example if "f" is defined as: ...
1
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0answers
64 views

How to do this integral of Hypergeometric functions in Mathematica?

I've tried to integrate by part, but it seems that Mathematica is still not able to integrate. ...
4
votes
2answers
304 views

Double integral

The question is Calculate the double integral where D is an area enclosed by the following lines, ,, and I have tried doing it the following way but its wrong and I cant seem to get it ...
3
votes
1answer
261 views

Plotting the 3D region that determines a volume

I need to plot this with Mathematica: Use a triple integral to determine the volume of the region below $z = 4 - x\,y$ and above the region in the xy-plane defined by $0 \leq x \leq2,\ 0 \leq y \...
8
votes
1answer
139 views

Symbolic and numeric limit disagreeing on branch cut of ArcTan

Bug introduced after v8.0.4 and before v9.0.1, and persisting through v10.4.1. Investigating comments to my previous question lead me to the following problem: ...
9
votes
1answer
162 views

Wrong limit: Limit[(1 + (-1)^n/n)^n, n -> Infinity]=1 (Mathematica 10.4 and W-Alpha)

Since $(1-\frac{1}{n})^n\to 1/e$ and $(1+1/n)^n\to e$, the sequence $(1+\frac{(-1)^n}{n})^n$ has no limit as $n\to\infty$, but has limits for odds and even numbers. If $n$ were taken to be real, there ...