# 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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### 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 ...
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### 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 ...
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### 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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### What does Mod^(1,0) mean in mathematica output [on hold]

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 ...
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### 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 ...
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### How to integrate with integer parameter in Mathematica?

I would like to integrate the following expression with N being Integer ...
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### 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 ...
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### How can the same Mathematica version give different symbolic results on different machines?

I'm testing the following code: ...
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### Compute score for a set of data [closed]

So let's explain my problem. I have a set of items which have a score from 0 to 100. This set is dynamic which means that several values are expected to be added from moment to moment. In each item is ...
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### 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 ...
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May I ask is there any wise way to calculate the following integration? $\int_{-1}^{1}\int_{-1}^{1}\int_{-1}^{1}\int_{-1}^{1}\frac{\left( 0.25 \left(-1+\eta _1\right) \eta _1 \left(-1+2 \eta ... 1answer 51 views ### Defining functions as derivatives I'm working on a model that requires a sum over a function that uses various coefficients. In order to make the sum easier to perform, I am trying to keep things general through the use of a ... 2answers 104 views ### Problems with integrating over a region Following the example of this answer: Find the volume of the region defined by$|x|+|y|+|z|<4$I tried to compute the following integral over a region by using ImplicitRegion. However, when I ... 1answer 3k views ### How to visualize Riemann surfaces? In WolframAlpha we can easily visualize Riemann surfaces of arbitrary functions, can we plot the Riemann surface of an arbitrary function using Mathematica and ... 2answers 114 views ### How to convolve the unit box function and the modified Bessel function of the second kind in 2D? In 1D the convolution of the unit box function and the modified Bessel function of the second kind$K_0(x)$works very well. ... 2answers 223 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 : ... 0answers 27 views ### NDSolve and Nintegrate give different plots of the same function? [closed] So my problem is that I transformed a differential equation to an integral equation and the results from Nintegrate is different from what I get with NDSolve. Shouldn't it be the same? I was expecting ... 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 ... 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: ... 1answer 50 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 ... 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 ... 0answers 17 views ### Module command and differential equation [duplicate] I write a programma see below ... 1answer 113 views ### From which version Mathematica will be available Symbolic n-th derivative? [duplicate] On www.wolframalfa.com Symbolic n-th derivative works. 1answer 144 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 ... 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 ... 3answers 385 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 ... 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 ... 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 ... 2answers 110 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, ... 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: ... 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 ... 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 ... 0answers 139 views ### Integrate producing bad result I noticed a bug in Mathematica. It computes incorrectly a definite integral ... 2answers 72 views ### Integral invoving product of Whittaker functions I'm trying to evaluate the integral $$\int W_{0,a}(x)\,W_{1,b}(x)\,\frac{dx}{x},$$ where$W$denotes the Whittaker$W$function, and$a,b\in[0,1/2]$. Using the Whittaker differential equations that ... 1answer 44 views ### I would like to be able to get this integral evaluation to show up in terms of variables this is very much a beginner question; I was hoping that someone may be able to take a look at this code and tell me why it outputs all of these crazy numbers instead of just the variables specified ... 0answers 60 views ### Cauchy Principal Value Cauchy principal value of the following integration gives nothing in Mathematica.$\int\limits_{-\infty}^\infty\frac{\text{dx}}{x-2}$I tried some hand calculation which is ... 1answer 38 views ### Maclaurin Series Help [closed] My problem is to numerically approximate the series (1 - Cos[x])/x over the interval [0,1]. I typed it into Mathematica as so: ... 1answer 70 views ### Faster code for calculat in Integral include derivative I saw this question How I can get faster I tried help that. But I can not understand. I want to write a faster code for: ... 2answers 138 views ### Definite integration in mathematica I tried to integrate the following in Mathematica.$\int\limits_{-\infty}^\infty\cfrac{\text{e}^{\text{i}ax}}{x^2-b^2}\text{d}x$where$a,b>0\$ The analytical result is well known. ...
I'm evaluating $$\lim_{z\to e^{i \pi/2 n}} \frac{z-e^{i \pi/2 n}}{z^{2 n}+1}$$ with Mathematica 9.0.1: ...