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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5
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2answers
262 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 ...
1
vote
1answer
88 views
0
votes
0answers
38 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
1answer
61 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
107 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 ...
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
84 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
60 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 ...
1
vote
0answers
17 views

Module command and differential equation [duplicate]

I write a programma see below ...
1
vote
1answer
120 views

From which version Mathematica will be available Symbolic n-th derivative? [duplicate]

On www.wolframalfa.com Symbolic n-th derivative works.
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 ...
2
votes
1answer
92 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 ...
2
votes
1answer
149 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 ...
6
votes
3answers
388 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 ...
1
vote
2answers
232 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 : $\textrm{...
3
votes
2answers
113 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, ...
2
votes
3answers
211 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 ...
3
votes
2answers
79 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 $...
0
votes
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 ...
2
votes
0answers
63 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 $\lim\limits_{\...
-1
votes
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: ...
0
votes
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: ...
3
votes
2answers
143 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. $-\cfrac{\pi}{...
0
votes
0answers
57 views

Learning Mathematica for Math Majors [duplicate]

I just downloaded Mathematica and I'm taking a course in Multivariable Calculus. I realize there is a lot of complexity to Mathematica and there are Many types of learning resources out there. I was ...
5
votes
0answers
68 views

Huge difference after changing a fraction to decimal

I have a limit to calculate. With[{p = 1/2, q = 0.1}, Limit[a^q Integrate[Sin[x]/x^p, {x, a, Infinity}], a -> Infinity]] gives correct result ...
3
votes
0answers
78 views

Wrong limit involving sine?

Using Mathematica 9.0.0.0, I was trying to calculate the sum $$ B_n = \sum_{i=1}^n \sin^4\left(\frac{(i-1)}{(n-1)}\cdot\frac{\pi}{2}\right). $$ where I thought it would be $B_n = \frac{3(n-1) + 4}{8}$....
0
votes
1answer
71 views

How to perform this nth derivative operation in MMA?

I have to solve this following equation where I need to differentiate a function $n$ times. $$A=\sum_{n=0}^{m-1}\frac{s^n}{n!}(-1)^n\frac{d^nf(s)}{ds^n}$$ How to express the above equation in ...
0
votes
0answers
38 views

Recycle boundary condition

I'm having the following issue that can not find a solution , by using this boundary condition u[0, t] == 2 u[1, t] that Mathematica does not understand, someone ...
5
votes
0answers
145 views

Integrate producing bad result

I noticed a bug in Mathematica. It computes incorrectly a definite integral ...
1
vote
2answers
111 views

Numerical integration does excessive coarse-graining?

I am trying to perform numerically the following integral $$\int_0^8\text{d}x\,\text{Re}\left[\frac{e^{-\frac{a^2}{2}-\frac{x^2}{2}} x^4 \sin (b x)\left(e^{-i c x} \text{erfc}\left(\frac{-c +i x }{\...
3
votes
1answer
46 views

Why does the following integral generate an error message for Delete::partw and Integrate`ImproperDump`tmp

The following integral generates a couple of errors that I'm not sure what they mean or how to prevent them ...
0
votes
2answers
84 views

Jump boundary conditions

I'm having the following issue that can not find a solution , by using this boundary condition ...
6
votes
1answer
153 views

Strange DiracDelta integration results in 10.4.1

Integrate[DiracDelta[s (x - c)] x, {x, -Infinity, Infinity}, Assumptions -> {s > 0, c > 0}] gives me c/s in ...
2
votes
1answer
70 views

Inconsistent Integrate behavior?

Evaluating the following integral with Mathematica Integrate[q0/(-1 + q0^2), {q0, 0, A}] gives a conditional expression ...
0
votes
2answers
138 views

The Disc and Washer Methods [closed]

How is it possible to demonstrate a visual solid of revolution utilizing the washer method? For example to show the shape formed by rotating the region bounded by $y=(x-2)^4, 8x-y=16$ about $x=10$? ...
5
votes
1answer
76 views

ComplexInfinity for a convergent product

The infinite product involving the ratio of (n^2)! to its Stirling approximation ...
3
votes
2answers
99 views

Are there any code which just derivative of piecewise function(same distence)?

I wrote this code: Piecewise[{{x^2, 0 <= x <= 1}, {x, x <= 4}}] and I got derivative of this code: ...
1
vote
2answers
52 views

Integration over variables

I'm trying to take the integration of 1/x over v0 and vt. I want it to output: Ln(v0 / vt) or at least Ln(v0) - Ln(vt). I tried ...
0
votes
0answers
31 views

Using assumptions with Integrate [duplicate]

I open Mathematica and execute this code: ...
0
votes
2answers
100 views

Numerical derivative from data points

I want to take the second derivative of a set of data points (at the point $x = 0$). Let's assume that this set looks like that ...
3
votes
1answer
55 views

Dirac delta in integrals

I am trying to simplify the following integral ...
0
votes
1answer
57 views

Partial derivative of function of two variables

This question is not enlightening nor is it difficult. But some part of my notation or how I have defined my functions is messing up the D[f,x] function. ...
1
vote
2answers
159 views

Why can't Mathematica integrate this PDF?

I'm trying to integrate a transformed Gumbel PDF in Mathematica. Integrate[E^(η*(-(x - q)) - E^((-η)*(x - q))), {x, t, ∞}] However, it doesn't compute. It's fine ...
1
vote
3answers
129 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
votes
1answer
106 views

Elliptic integral of the first kind [closed]

I want to plot the integral $$I(\phi) = \int_0^{\phi} \frac{\mathrm{d} \theta}{\sqrt{1 +\sin(\theta)^2}}$$ In Mathematica notation, it is a case of an elliptic integral of the first kind with $m=-1$, ...
2
votes
1answer
106 views

Maximize a variable in NSolve Function

I want to solve a set of trigometric coupled equations with the NSolve funcion while at the same time trying to maximize a variable which has to be real and between ...
7
votes
2answers
166 views

Sets and sums of different elements

Consider the set S={w,x,y,z}. If the set of all possible sums of any three different elements from S is {-1,3,5,8}, then what is the set S? How could I solve this function using Mathematica?
1
vote
1answer
37 views

How to specify assumptions without typing out functions

So I want to add assumptions in carrying out integration. I know I could use the Integrate function: Integrate[V Exp[-x/a] ,{x,0,10}, Assumptions->a>0] but ...
0
votes
1answer
145 views

Solving integral

How can I solve this integral: Integrate[expression, x] where expression is: ...
5
votes
2answers
237 views

Orthogonalize polynomials with respect to Gagliardo seminorm?

For a function $f\colon [-1,1]\to\mathbb{R}$, the Gagliardo seminorm of $f$ is defined to be $$ |f| = \int_{-1}^1\int_{-1}^1 \frac{(f(x)-f(y))^2}{(x-y)^2}\, \mathrm{d}x\, \mathrm{d} y. $$ Given $(x,...