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
22 views

How I can Integrate this in Mathematica?

How can I get the solution of this integrate below ? $$\int_0^{a} x e^{-\frac{b^2 x^2}{2 c}} J_0(n x) dx$$ where $a,b,c$ and $n$ are constants and $J_0$ is the Bessel functions of the first kind of ...
-1
votes
0answers
26 views

Differentiation and integration [on hold]

When I differentiate y, I get: $$y=(x+1)^2$$ $$\frac{dy}{dx}=2x+2$$ When I try to integrate this differential I get: $$y=x^2+2x+C$$ I see that this is incorrect, but I don't understand why. How in ...
3
votes
3answers
116 views

Calculating $\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$

How can we force Mathematica to compute this limit? $$\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$$ It seems it ...
1
vote
0answers
27 views

Converting integral equations to differential equations [on hold]

I am trying to use Mathematica to convert integrals to differential equations, of any order. Could you please advise as to the command to use, and the format?
0
votes
0answers
42 views

Bounds of a closed curve

how to find the rectangular bounds of a curve which is of the form f(x,y) and forms a closed loop. The sides of the rectangle are parallel to the axes and are tangents to the curve. The time taken for ...
0
votes
0answers
25 views

Limit of form 1 raised to infinity [on hold]

Right hand limit of any limit of the form 1 raised to infinity should always come out to be infinity and left hand limit of 1 raised to infinity should come to be 0 . why do we get other values as ...
3
votes
2answers
125 views

Analytic expression for a Complex Hilbert Transform in Mathematica

I need to solve the following integral equations for a problem I'm working on - $\frac{-i}{2 \pi}$ $\int_{-a}^{a} \mathrm{dt}\,\, \frac{e^{i k t}}{t + i \tau}$ and $\frac{-i}{2 \pi}$ ...
-4
votes
0answers
57 views

Lesson 3, Try it 05, 6a [closed]

At time t, an object is given to be at a point P[t] = {x[t], y[t]} Its velocity at time t is just velocity[t] = D[P[t], t] ...
0
votes
1answer
53 views

Strange behavior of `FourierSinCoefficient`

FourierSinCoefficient works normally like this and the result is checked with Integrate. ...
0
votes
0answers
51 views

Why the derivative of $e^{kx}$ yields two different results on Mathematica and W|A? [closed]

I did the following on Mathematica: D[E^kx, x] And it yields zero. Now asking for the W|A input on Mathematica, it gives me: $\quad \quad \quad \quad \quad ...
4
votes
1answer
72 views

Formal Differentiation

I'm trying to formally differentiate an expression. (I am aware of how to differentiate formally?, but am unable to generalize the idea) For example: ...
2
votes
1answer
114 views

Integration doesn't work

I'm trying to obtain the following integral: ...
0
votes
1answer
39 views

How to simplify and evaluate Integral with lots of DiracDelta dists

I have a question about an Integrals which I can do by hand but I want to implement this Integral in Mathematica. Actually it is the definition of a 2 Particle Phase Space. The Expression is the ...
4
votes
0answers
67 views

Confirming conservation laws for complex valued functions

Consider the nonlinear Schrödinger equation (I would like to do this for a more complicated set of equations, but to gain understanding I'll consider this simplified case) $$A_t+iA_{xx}+i|A|^2A =0,$$ ...
0
votes
0answers
65 views

Multiple integral not evaluating for large number of independent variables

Problem I want to evaluate the following integral, first over each $x_i \in [0,s]$ and then over $s \in [0,\infty)$. \begin{align*} I_1 = \int_{0}^{\infty} \idotsint_V ...
0
votes
0answers
55 views

PolyLog does not simplify

How come mathematica can not simplify a simple expression involving the PolyLog function? An example is: You know that ...
9
votes
2answers
203 views

Asymptotics of $\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}}$

I am fairly sure that asymptotically $$\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}} \sim \frac{2}{\pi n}.$$ I tried ...
1
vote
1answer
85 views

Dealing with Norm, Complex situation not desired

I am working on a notebook for my calculus students and am dealing frequently with the norm of vector valued functions. I always seem to run into this kind of situation. ...
1
vote
1answer
76 views

Absolute uncertainty and error propagation with lists [closed]

I am trying to do some error propagation using mathematica. This is my second day using the program. I am trying to take the derivative of a numerical function that is made up of the following lists. ...
10
votes
2answers
135 views
5
votes
1answer
121 views

How to do automatic differentiation?

Does Mathematica have any AD functionality or does it only support symbolic differentiation? If not, are there any packages or other third party implementations available? Edit (J. M.) Here is an ...
0
votes
0answers
45 views

Sharp Ratio Maximization, Closed Forms

I am trying to get a closed form for the following first order conditions (n=4): Here's the nb-File. The code is as follows: ...
6
votes
1answer
208 views

Solving $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$

I would like to solve the following equation: $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$ I have already posted it here, but still it doesn't work for me (I ...
2
votes
2answers
148 views

Two ways to speed up slow Integrate[]s? (Can't do either)

I run into problems like this all the time on the complicated integrands I pass to Integrate. The following code works but takes a veeery looong time: ...
0
votes
0answers
47 views

NIntegrate unexpectedly returns complex number

I am attempting to visualise the effect of shift parameter $\gamma$ on the 3-parameter log-normal distribution. $$pdf(x;\mu,\sigma,\gamma) = ...
1
vote
1answer
39 views

How to find all gaps of a domain of a function with Mathematica 9?

I tried it liek this: My test-function: fuu[x_] := Expand[FullSimplify[1/x]] how i find the domain: ...
0
votes
0answers
18 views

Not Simplify automatic some expression(values)

I try to calculate $$\text{res}\left(h(z) (\psi ^{(0)}(z)+\gamma )^2,\{z,-4\}\right)$$ the result is $$\frac{1}{6} \left(6 h'(-4)-25 h(-4)\right)$$ the result it is possible to write as $$2 \left(6 ...
8
votes
2answers
505 views

Weird plot with SphericalPlot3D

Taking the equation $x^2-y^2-z^2=1$ and using ContourPlot3D: ContourPlot3D[ x^2 - y^2 - z^2 == 1, {x, -3, 3}, {y, -3, 3}, {z, -3, 3}] Yields the proper image. ...
6
votes
2answers
146 views

Different results of the integrate $\int \frac{\sin (\pi s)}{(s-0.5)^2+90} \,ds$?

Following results are given of big different values. I think NIntegrate's one is right but others are not explained. ...
3
votes
1answer
105 views
2
votes
0answers
47 views

Better to have infinities in limits or integrands (`NIntegrate`)? [closed]

I'm using ListPlot to plot the integral of a function with respect of the function's second variable: ...
0
votes
0answers
28 views

Does a very large prefactor affect NIntegration time when plotting the result?

I'm using ListPlot[ NIntegrate[f[x,#],{x,a,b}]&/@Range[10,100] ] to plot the integral of the two variable function f as a ...
2
votes
1answer
87 views

Numerically integrate and plot $f(x;p)$ for a range of the parameter $p$

Suppose we have an integral of the form $$I = \int_a^b dx \, \sin(px), \tag{1}$$ where I've take $f(x;p) = \sin (px)$ to be specific. I want to plot this integral for a range of values of the ...
3
votes
2answers
115 views

How much time should one give Mathematica for an integral evaluation?

Sometimes when I do integrals in Mathematica (M), it keeps thinking and thinking and I have no idea what is going on inside M. For how long should one wait or how does one know whether M has not got ...
1
vote
0answers
35 views

Which type of integrals are better for Mathematica [closed]

Is it in general better to type in a integral with its limits, or is it better to type an indefinite integral into Mathematica? With better I mean: Likelihood that Mathematica can solve it, ...
0
votes
1answer
55 views

repeat calculate [closed]

I want to calculate the below program x[t+1].But I can only calculate t=0,1. please tell me how to calculate t = 0 to 10. ...
9
votes
1answer
228 views

Laplacian and DiracDelta

It is known that: $\nabla^2 \dfrac{1}{|r-r'|} = - 4 \pi \delta^3(\vec{r}-\vec{r}')$. If I do that with Mathematica, I find: ...
6
votes
1answer
101 views

Traces of the level surface $z=4x^2+y^2$

I came up with this method to plot the traces of the surface $z=4x^2+y^2$, in this case for $z=1$, 2, 3, and 4. ...
0
votes
2answers
107 views

Given integral, how to plot

I want to use mathematica to visualise some plots, this would help me understand my calculus course. My problem is this: Given that x^2 + y^2 <= a^2 Find ...
5
votes
3answers
206 views

Derivative of contour in ContourPlot

Sorry to bring this question up again, since there are many similar questions on the site. I use to think this is a easy job to do, because for the worst case I can follow the answers on this site. ...
8
votes
2answers
290 views

Why Mathematica cannot apply The Fundamental Theorem of Calculus automatically?

For some reason Mathematica cannot evaluate this definite integral: ...
4
votes
1answer
114 views

Fitting a Parametric Curve

I apologize if this question is obvious or simple. Im in HighSchool and have started playing around with Mathmatica only recently. For my Calculus Final I am suppose to use rotation about the y axis ...
2
votes
1answer
44 views

Meaning of Pattern at derivatives of arbitrary functions

I want to derivate some general functions like D[F[x[r_, p_], y[r_, p_]], r] or this simpler one D[F[G[x_]], x] . When I ...
0
votes
0answers
64 views

Using Manipulate to determine intersection of two surfaces

Here is what I have done thus far: ...
2
votes
2answers
121 views

Strange Boundary NDSolve Problem

Mma10.1 doesn't work with the following boundary problem: ...
10
votes
6answers
703 views

Integrate gives wrong results

Integrate[a/(Sin[t]^2 + a^2), {t, 0, 2 Pi}] $$\int_0^{2 \pi } \frac{a}{a^2+\sin ^2(t)} \, dt$$ gives $0$ This cannot be true. What is going on? If I insert a ...
9
votes
2answers
207 views

Volumes of Revolution with detailed diagram

All, In calculus I have to do images such as the following in helping explain technique to students. This one is by rotating $y=\sqrt x$ about the x-axis, an image copied from Stewart's Calculus ...
0
votes
0answers
7 views

Some expectations of psi (digamma) function [migrated]

I want to derive an Expectation-Maximization algorithm for my model. But some expectations of psi (digamma) function is needed in the procedure. Assuming I have a Gamma distributed random Variable ...
0
votes
0answers
9 views

One point following another moving in a straight line? [migrated]

There is a plane with two points on it, let's say A and B. A starts at an arbitrary constant point, let's say (0, 0), and B at a point that needs to be tested, which we'll call (c, d). A moves ...
1
vote
1answer
54 views

Adding a title that includes angle between two vectors in Graphic in Manipulate

Here is what I have tried thus far: ...