Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

learn more… | top users | synonyms (3)

0
votes
0answers
43 views

Performing numerical derivative after numerical integration

First of all, I am sorry to repeat a question which is similar to the closed question, "Numerical Derivative after numerical integration". I could not understand the solution introduced in the link. ...
0
votes
0answers
35 views
4
votes
2answers
274 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
237 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
104 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
153 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 ...
0
votes
0answers
47 views

Functions with indexed variables [on hold]

This Solve[{A/x - l p == 0, A/y - l q == 0, x p + y q == R}, {x, y, l}] but I wonder if it is possible to replace $x$ by $x_1$, $y$ by $x_2$, $p$ by $p_1$ et $q$ ...
8
votes
1answer
105 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 ...
7
votes
2answers
298 views

Can your Mathematica do the following integral?

Backslide introduced in v10 and fixed in v10.4.1. I was trying to do the following integral in Mathematica: Integrate[(z-2) PolyLog[2,z]Log[1-z]/z^3,z] What I ...
-3
votes
1answer
68 views

How can I fix my code? [on hold]

I am running this following code in Mathematica. It shows some error message. I have no problem with it. But it does not show the output for $m=1/2$. It shows me the output when $m=1$ and $m=2$. How ...
1
vote
1answer
37 views
0
votes
0answers
28 views

A simple question on recuperation of a result [closed]

It's perhaps an already ask question and perhpas it is stupid, but I do not know how to search for it. If sol = Solve[a x^2 + b x + c == 0, x] when calling ...
0
votes
2answers
52 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 ...
0
votes
2answers
94 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 ...
0
votes
1answer
372 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 ...
2
votes
0answers
56 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 ...
10
votes
1answer
233 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 ...
1
vote
1answer
59 views

How to integrate with integer parameter in Mathematica?

I would like to integrate the following expression with N being Integer ...
0
votes
0answers
68 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_{- ...
11
votes
3answers
253 views

Integrating a BesselJ integrand to obtain the same result as Maple 16

I would like to check the following integration: Integrate[y Integrate[1/x BesselJ[1, x Exp[I π/4]] BesselJ[1, x Exp[-I π/4]], {x, 0, y}], {y, 0, r}] ...
0
votes
0answers
50 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
0answers
3 views

Double Integral Range [migrated]

we want the Surface between the two equation: $r= 1 + cos\theta$ $r = 1$ (circle) we can use a duble integral to solve this: $$ S = \int_{-\pi/2}^{\pi/2} \int_1^{1+cos\theta} r \,dr\,d\theta $$ ...
2
votes
1answer
67 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 ...
3
votes
1answer
454 views

Gâteaux (directional) derivatives and higher order differentials of a functional

I would like to calculate the Gâteaux derivative of a functional (i.e. a function depending on functions). A simple example for the Dirichlet functional: $L(u(x))=\int_0^1 \frac{1}{2} (u'(x))^2 dx$ ...
5
votes
2answers
252 views

Strange phenomenon occurring in analytic integration result involving Bessel functions

For the following integral, Integrate[x^2 Exp[-a x^2 - b x^4], {x, -∞, ∞}, Assumptions -> {a > 0, b > 0}] Mathematica gives the following analytic ...
0
votes
1answer
233 views

Asymptotic forms of Bessel function

I want to replace Bessel functions by asymptotic forms, so the question is: can I find the best ones with help of Mathematica? And if it's possible, how can I do it? Update How can I get with ...
5
votes
0answers
109 views

MacDonald formula for Modified Bessel Functions

How can I make Mathematica understand these two integrals? $$\int_0^{\infty} e^{-x \cosh{\xi}} d\xi = K_0(x)$$ $$\int_0^{\infty} e^{-\frac{1}{2} \Big( \frac{x y}{u} + u \frac{x^2+y^2}{x y} \Big) } ...
0
votes
0answers
36 views

Replace higher order derivatives given lower order derivative

I have an unknown function f[x1,x2] whose partial with respect to x1 is identically zero. I would like to make sure that ...
1
vote
3answers
110 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 ...
1
vote
1answer
51 views

Defining functions as derivatives

I'm working on a model that requires a sum over a function that uses various coefficients. In order to make the sum easier to perform, I am trying to keep things general through the use of a ...
3
votes
2answers
104 views

Problems with integrating over a region

Following the example of this answer: Find the volume of the region defined by $|x|+|y|+|z|<4$ I tried to compute the following integral over a region by using ImplicitRegion. However, when I ...
28
votes
1answer
3k views

How to visualize Riemann surfaces?

In WolframAlpha we can easily visualize Riemann surfaces of arbitrary functions, can we plot the Riemann surface of an arbitrary function using Mathematica and ...
1
vote
2answers
114 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. ...
1
vote
2answers
228 views

How to compute this integral?

I'm trying to calculate this integral : $$I(z,k,a)= \displaystyle\int_{1}^{\infty} t^2\, \text{ArcTanh} \left(\sqrt{\frac{t^2-1}{t^2}} \dfrac{k}{z}\right)\, e^{-a\,t} \, dt$$ Where : ...
10
votes
1answer
1k views

How does a Pringle lose its curvature?

Nom! As part of a bigger project, I've was writing some code to calculate the scalar curvature of surfaces of the form $z = f(x,y)$. This uses a general calculation of the scalar curvature to produce ...
0
votes
1answer
82 views

Tedious integral

I'm new to Mathematica so I'm not familiar with its potential use to solve tedious symbolically integrals. I'm trying to solve the following one: ...
0
votes
1answer
52 views

integral involving square of exponential integral

I'm trying to compute the integral $$ \int_{a}^{\infty}\frac{e^x}{x}[\mathrm{Ei}(-x)]^2\,dx, $$ where $\mathrm{Ei}$ is the exponential integral, and $a>0$. The obvious ...
4
votes
1answer
1k views

How to take the derivative w.r.t. an arbitrary function?

EDIT: The answer posted by @Jens works for built-in functions only. However I'm starting to wonder if this is related to my Mathematica install somehow. I have version 7. Here is an example in the ...
1
vote
0answers
17 views
2
votes
1answer
145 views

How to linearize an expression involving derivatives?

I want to linearize the expression involving function $y(x,t)$ $$[y^3(y_x-y_{xxx})]_x$$ by assuming $y(x,t)=y_0(t)+y\prime(x,t)$, where $y\prime(x,t)$ is a small variation. In other words, I will ...
0
votes
1answer
43 views

Assumptions with Multiple Rules

What is the correct way to add more than one assumption while integrating? I am attempting to evaluate the following integral and Mathematica is just stalling, so I'm wondering if my assumptions are ...
6
votes
3answers
386 views

Integrate to calculate enclosed area

I am trying to 'use an integral in polar coordinates to calculate the area enclosed by this curve': The curve is: r=sin2θ, θ ∈ [0, π] which I believe is already in ...
2
votes
1answer
89 views

Dog chases his tail ! - “parametric differential/Integral equation”..?

I have the following situation where I am interested in the function $m(t)$ $$ \frac{dm}{dt}=4T(t)^{3}+T(t)^{2} $$ $$ T(\tau)=T_{0}-\int_{0}^{\tau}(\frac{dm}{dt})dt*Q_{S} $$ Is there a way to solve ...
1
vote
1answer
130 views

Differential Equations and Unit Notation

What do I get the Syntax::sntxi: Incomplete expression; more input is needed . error when I try to use the math palette for derivatives? What does the dot in ...
3
votes
2answers
112 views

How to plot a volume for triple enclosed by surfaces

My main issue (multivariate calculus), I want to plot the body made within the surfaces y + z = 4, y = 4 - x^2, ...
4
votes
1answer
184 views

Why can't the Bernstein Bears work normally?

Bug introduced in 7.0 and fixed in 9.0 I want to use the built-in BernsteinBasis[] to learn about Bezier curves. I tried the following code: ...
2
votes
3answers
197 views

Mathematica Integration Problem

I am new user of Mathematica. Can anybody help me to solve this integration? I really needs your help. Integrate[(1 - (1/(1 + A x^(-ao)))) x, {x, 0, r}] Can not ...
14
votes
2answers
1k views

Getting an InterpolatingFunction from a ContourPlot

I have a function, say minimizeme[Ω_][β_][ϵ_] = ϵ^2 Ω - Log[2 (Cosh[2 β] + Cosh[2 β ϵ])]/(2 β); I want to find its critical points in $\epsilon$ for a given ...