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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2
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0answers
24 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
votes
0answers
26 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 ...
0
votes
0answers
21 views

Trouble evaluating an integral for certain parameters

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
90 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
votes
1answer
47 views

Can this expression be calculated symbolically?

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

How to compute this integration?

I would like to compute the following integral: I tried to write it as ...
1
vote
1answer
78 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 $t$, ...
3
votes
3answers
253 views
2
votes
2answers
115 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
votes
0answers
49 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
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 ...
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, ...
-2
votes
0answers
35 views

How to compute a integrate a triple integral? [closed]

I have tried to compute this triple integral but I keep getting an error. I have attached a picture of my code.
1
vote
1answer
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 ...
0
votes
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
votes
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, ...
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 ...
0
votes
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 ...
0
votes
0answers
41 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
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 ...
3
votes
1answer
96 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/\...
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 ...
0
votes
1answer
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] ...
3
votes
2answers
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: <...
3
votes
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
2answers
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. ...
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 ...
1
vote
0answers
63 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
303 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
260 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: ...
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 ...
1
vote
1answer
51 views

nonatomic expression expected when trying to sum of the integrals of two functions

newbie to MMA. After computing the following two integrals: ...
0
votes
2answers
54 views

Issue while trying to compute the integral for the coefficients of a triangular wave

I was trying to compute these integrals in order to check if I was correct: or in code ...
2
votes
0answers
58 views

What does Mod^(1,0) mean in mathematica output [closed]

I am trying to take he derivative of mod(remainder). In:= D[Mod[x, y], x] Out = Mod^(1,0)[x,y] I cannot understand the meaning of Mod^(1,0). What does the ...
0
votes
2answers
101 views

Integral over real valued function becomes complex

I've tried to solve the following integral, but I get a complex solution even tough it should only have a real part. $$f(x)=- \frac{10^{-20} x}{0.99005- e^{10^{-12}x}}$$ Now I want to calculate the ...
1
vote
1answer
63 views

How to integrate with integer parameter in Mathematica?

I would like to integrate the following expression with N being Integer ...
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 ...
10
votes
1answer
246 views

Vastly incorrect answers obtained by increasing WorkingPrecision with modified Bessel functions

Bug introduced in 7.0 or earlier and persisting through 10.4.1 This is a follow-up to this question regarding numerical instabilities occurring with modified Bessel functions. In trying to explore J....
0
votes
0answers
71 views

Tricky inverse Laplace transform

I'm trying to compute the inverse Laplace transform of $f(s) = s^c/(N + s^{ir} )$ where $c,N \in \mathbb{C}$ and $r \in \mathbb{R}^+$ using the Bromwich integral $$ F(t) = \frac{1}{2 \pi i} \int_{- ...
0
votes
1answer
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 ...
2
votes
1answer
78 views

Why does NDSolve and NIntegrate not give the same result? [closed]

I have plotted solution of two equivalent equations one in Integral form (right chart) the other in Differential form (left chart) using NDSolve and NIntegrate but they give me completely different ...