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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1
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2answers
61 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
130 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
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1answer
153 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
2answers
308 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
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1answer
82 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 ...
3
votes
3answers
134 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
80 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
46 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
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2answers
130 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
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1answer
71 views

Strange behavior of `FourierSinCoefficient`

FourierSinCoefficient works normally like this and the result is checked with Integrate. ...
4
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1answer
76 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
118 views

Integration doesn't work

I'm trying to obtain the following integral: ...
1
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1answer
80 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 ...
5
votes
1answer
162 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
56 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
246 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 ...
2
votes
2answers
117 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
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1answer
84 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
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2answers
141 views
6
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1answer
149 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
48 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
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1answer
212 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
156 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
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0answers
49 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
530 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
151 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
114 views
2
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0answers
48 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
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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
97 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
122 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
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0answers
38 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
61 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
240 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
110 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
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2answers
112 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
221 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
299 views

Why Mathematica cannot apply The Fundamental Theorem of Calculus automatically?

For some reason Mathematica cannot evaluate this definite integral: ...
4
votes
1answer
128 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
51 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
66 views

Using Manipulate to determine intersection of two surfaces

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

Strange Boundary NDSolve Problem

Mma10.1 doesn't work with the following boundary problem: ...
10
votes
6answers
732 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
210 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 ...
1
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1answer
56 views

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

Here is what I have tried thus far: ...
0
votes
0answers
39 views

Integration problem: lrgexp

I want to calculate the following integration but it gives the error PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD. The code is: ...
1
vote
2answers
63 views

Derivative of Continuous and Differentiable Piecewise function is indeterminate

I'm attempting to analytically stitch together two linear functions with two quadratic functions. The function I'm considering, then, is a piecewise function consisting of 4 parts. Below are the ...
0
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0answers
65 views