# Tagged Questions

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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### Mathematica implementation of Zeilberger's algorithm (previously done in Maple)

I have this Mathematica code: ...
383 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 ...
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### 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 ...
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### 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 ...
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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### 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 <...
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### 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 ...
131 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 ...
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 ...
124 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 ...
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, ...
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129 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] ...
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 ...
134 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: <...
82 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 ...
92 views

### How to set a line coordinate for a symbolic line integral over a curve? [closed]

I have the following closed curve, defined by a set of points. ...
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### 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 ...
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### 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 ...
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: ...
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. ...