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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1answer
53 views

Implicit derivatives in one line ,How do I do it?

I have this little script to derive implicitly Mathematica $PrePrint = # /. {D[y_, x_, NonConstants -> {y_}] :> y'[x]} &; Example ...
2
votes
0answers
49 views

Minimax for conditioned UnitStep functions

I made a simplified version of my problem, and I have now: ...
-3
votes
0answers
53 views

Find the tangent at a homogenous point to a curve [on hold]

I'm new to Mathematica. I want to find the tangent at the point $p=(6,5,1)$ to the following curve: ...
3
votes
1answer
67 views

How do I color Riemann integral rectangles using conditionals?

I'm builind a function to visualize the Riemann Integration process to any function using rectangles. Everything is fine, except that I need the color of the rectangles to change if they're under the ...
-4
votes
0answers
36 views

measure theory : Lebesgue measure [on hold]

let E subset of the IR ..if m*(E)=0 then m*(E^2)=0 E^2={ x^2 : xεΕ } can you give me a hint please? Blockquote
2
votes
2answers
122 views

MaxValue of a periodic function

I want to find the maximum of a periodic function on the interval [-Pi,Pi]. What I tried is the following: ...
6
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3answers
179 views

Limit of Nested Radical $\sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+…}}}$

I want to find limit of infinite nested radical $\quad \quad \sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+...}}}$ but I don't know how to define this expression in Mathematica. How can I define it and ...
5
votes
1answer
196 views

Need help with the Lagrange multiplier method

Well I am new to Mathematica and got really stuck solving this problem. In class, I was ask to use the Lagrange multiplier method to find the maximum and minimum value of $f(x,y) = x^2+y^2$ which ...
1
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2answers
78 views

Ask about the variable and constants in partial derivative in a loop

EDITED I have a function in a list like : func={2(x^2)+x*y+3(y^2)}; I want to have a UI that ask me which parameter (x or y) is a variable in a ...
6
votes
2answers
198 views

Curvature Application

I found these amazing animations at https://courses.engr.illinois.edu/tam212/avt.xhtml#avt which I think will be wonderfully useful when teaching multivariable calculus next semester. I've started to ...
1
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2answers
59 views

How to tell Mathematica that a limit converges to a product of two variables

I have looked through the manual and Im simply just stuck trying to make Mathematica solve this: ...
4
votes
3answers
125 views

How to get multiplication of the elements of a specific list/Matrix

Assume there is a list: List1={a,b,c,d}; Then I want to get these calculation: ...
6
votes
1answer
148 views

Defining a function implicitly and calculating its derivatives

I'm interested in using Mathematica's symbolic manipulation to obtain, for a particular function $f$, derivatives of arbitrary order evaluated at zero. Normally I'd use the ...
2
votes
1answer
221 views

How I can integrate $\int_0^{a} x e^{-\frac{b^2 x^2}{2 c}} J_0(n x) dx$?

How can I get a solution to the integral given below ? $\quad \quad \int_0^{a} x e^{-\frac{b^2 x^2}{2 c}} J_0(n x) dx$ where $a,\,b,\,c$ and $n$ are constants and $J_0$ is a Bessel function of the ...
0
votes
1answer
79 views

FullSimplify not giving me a physically useful answer for Mott scattering

I am using Mathematica to find the cross-section for Mott scattering over an extended target. I evaluated ...
-1
votes
0answers
31 views

Differentiation and integration [closed]

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
132 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 ...
2
votes
0answers
75 views

Converting integral equations to differential equations

I am trying to use Mathematica to convert integrals to differential equations, of any order. An example of an integral equation is given below, in Mathematica code. Could you please advise as to the ...
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 ...
3
votes
2answers
127 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 $\frac{-i}{2 \pi}$ ...
0
votes
1answer
55 views

Strange behavior of `FourierSinCoefficient`

FourierSinCoefficient works normally like this and the result is checked with Integrate. ...
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
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1answer
116 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
1answer
150 views
+50

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
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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 ...
10
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2answers
239 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
86 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
80 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
136 views
5
votes
1answer
122 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
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0answers
46 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
209 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
152 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
511 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
148 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
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1answer
107 views
2
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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
88 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
116 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
56 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
231 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
102 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
108 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 ...