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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13
votes
1answer
169 views

Teaching Mathematica more about DiracDelta and KroneckerDelta

As the documentation and some experimentation indicates, Mathematica contains little information about representations of the DiracDelta and ...
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
1
vote
2answers
160 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 ...
0
votes
2answers
281 views

Why the result by hand is different from the built-in DSolve?

Yesterday, I used Mathematica to solve a differential equation using the built-in command DSolve[]: ...
0
votes
2answers
103 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 ...
2
votes
1answer
109 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 ...
3
votes
1answer
55 views

Dirac delta in integrals

I am trying to simplify the following integral ...
5
votes
2answers
163 views

Derivatives of piecewise functions of functions

Background Derivatives of piecewise functions in Mathematica are computed according to special rules. According the Piecewise documentation (see Possible Issues), ...
0
votes
1answer
63 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. ...
0
votes
1answer
109 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 $m=-1$, ...
5
votes
4answers
247 views

Results in terms of a function

Let's assume I have a function $f(x)=\exp(10x^2)$, i.e. f[x_]:= Exp[10*x^2]. When I differentiate $f$ by evaluating the expression ...
7
votes
2answers
169 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
148 views

Solving integral

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

Any reason why this definite integral is so slow to compute and the indefinite fast?

This integral is easy and fast to compute Integrate[Sqrt[(x^2) + k ], x] $$\frac{1}{2} x \sqrt{k+x^2}+\frac{1}{2} k \log \left(\sqrt{k+x^2}+x\right)$$ But ...
10
votes
1answer
479 views

Compute inverse Laplace transform with Integrate

Since inverse Laplace transform is just an integral, while we already have InverseLaplaceTransform built in, can we compute it with ...
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,...
1
vote
1answer
64 views

How to find the pole of a equation where the residue exist?

I want to calculate the residue of an equation, such as: equ = 1/((x - 2)Sqrt[x - 1]) So first I need to find the pole of the equation. My method is find the ...
8
votes
1answer
210 views

Strange result of parameter-dependent definite integral

Inspired by this question on Math.SE, I wanted to see what Mathematica could do with the integral $$ \int_0^{\pi}e^{k\cos t}\cos(k\sin t)\,dt. $$ Thus, I entered into Mathematica (tried on both 10.3 ...
0
votes
1answer
106 views

Solving this equation with NDSolve

I'm trying to solve a differential equation numerically. I've written this code but it is leading to some errors "initial history needs to be specified for all variables for delay-differential ...
2
votes
2answers
455 views

How to find the area between 3 curves?

I have three equations: $y=3/x$, $y=12x$, and $y=x/12$, $x>0$. I am not sure how to go about integrating an equation once I find the intersections. Do I need multiple integrals?
6
votes
1answer
131 views

Animate the line integral over a scalar field

There is a gif from Wikipedia, The line integral over a scalar field $f$. How to plot and animate this in Mathematica?
0
votes
1answer
86 views

Integral not giving expected answer [closed]

Below is the integral I'm trying to evaluate: ...
4
votes
2answers
175 views

How does Mathematica calculate integrals? [duplicate]

One can use mathematica to get $$ \int_{-\infty}^{\infty}\frac{\sin^2x}{x^2+1}\ dx=\frac{\pi \sinh 1}{e}. $$ Here are my questions: [Edited:] Is there a way that I can see the intermediate steps ...
5
votes
1answer
413 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
5
votes
2answers
191 views

Definite integral closed-form expression

Is there a way to get Mathematica yield a closed-form expression (in terms of special functions) for the integral: $$ \int_{0}^{\infty} e^{-a t}\log(t)\log(1+t)\,dt, $$ where $a>0$? The obvious <...
1
vote
2answers
120 views

How to find the limit of a function of two variables

I was wondering if there is a method to find the limit of a function of two variables at a point. I tried the following: ...
-2
votes
1answer
92 views

How would I find the area of a function over a specific interval? [closed]

How would I find the area of a function over a specific interval? For example: $g(x) = e^{5x}$ Find the area of the function over the interval $[-4, 2]$.
1
vote
1answer
170 views

How I can get faster code for computing a fractional integral?

I use of this code Fractional Integral and wrote the following code: ...
1
vote
0answers
61 views

Limit not evaluated [closed]

I hope this question ha not been asked since the limit is evaluated in 1 not at 0 or infinity. I do not know how to ask Mathematica to find the limit as n -> 1 of the following function: ...
0
votes
1answer
78 views

Rotate from 0<=X<infinity [closed]

Find the volume of the solid obtained by rotating the region below the graph of y = e^(−x) about the x-axis for 0 ≤ x < ∞ With that given expression I tried to do it by doing the following code: ...
6
votes
2answers
182 views

Probability of distance of two random points in the unit circle

Inspired by the problem solve this probability problem symbolically which I have already generalized there I'd like to ask here the same question for a unit circle. More precisely: given two randomly ...
0
votes
0answers
60 views

Sum of Infinite convergent series

I have a series as Sum[(x^1 - (x - 1)^1) (b^Log[(1 + (x))]), {x, 1, Infinity}] which is convergent when b=0.3 and ...
0
votes
0answers
23 views

Syntax Error with Expectation over Distribution

I am getting some errors when I try to execute the following code. Here, the expectation is taken over $g$ which has Nakagami Distribution. ...
-1
votes
1answer
104 views

Double integrals in quantum chemistry [closed]

In quantum chemistry we often encounter integrals like this: I can't understand what is the problem. Can anybody help me?
0
votes
1answer
70 views

Why does Mathematica 10.3.1 fail me on : Integrate[(x^3) [Log[2 Sin[x]]]^8, {x, 0, Pi}] [closed]

All it gives me is a pretty restatement of my original request. When I use WolframAlpha PRO, I get a result of 624510 and a visual representation of the area in question. I know the ends of the ...
13
votes
5answers
517 views

solve this probability problem symbolically

Consider a unit square, Pick two points P and Q uniformly at random inside the square, What is the probability that |PQ|>1? I tried solve this problem ...
3
votes
1answer
110 views

Calling Integrate with many limits of integration

I accidentally discovered that you can put many numbers into the limits of integration of Integrate and Mathematica will still evaluate it without returning an ...
4
votes
3answers
195 views

How to solve this integration? [closed]

I need to find the integration of the following expression $$H(k)=\frac{\tau_0}{\pi}\int_0^{\infty}\exp\left(-u^{\delta}\cos\left(\frac{\delta\pi}{2}\right)\right)\cos\left(u^{\delta}\sin\left(\frac{\...
0
votes
2answers
94 views
4
votes
1answer
90 views

Am I getting a correct answer with the Dt command?

We are asked to find $dy/dx$ when $x^y=y^x$. Our hand calculations use logarithmic differentiation. $$\begin{align*} x^y&=y^x\\ \ln x^y&=\ln y^x\\ y\ln x&=x\ln y\\ \end{align*}$$ Then we ...
9
votes
3answers
452 views

Pulling constants out of integrations [duplicate]

The following is the code and output of a Mathematica command How do I get Mathematica to remove $g(y)$ outside the integral?
2
votes
3answers
104 views

How to find nth log derivative using mathematica?

Now I have a function, say $f(k,z)=e^{-kz}(1+kz)$ I want to find the $n$th $\log$ derivative with respect to z. like $(z\partial_z)^{(n)}f(k,z)$ (or $(\partial_{\ln z})^{(n)}f(k,z)$ if you like), ...
8
votes
2answers
857 views

Numerical contour integrations in the complex plane - contour deformation gives different answer for analytic kernel

I am trying to do a contour integration in Mathematica numerically. In particular, I'm checking the identity: $$ H_m^{(1)}(z) =\frac{i^{-m}}{\pi}\int_{-\pi/2 + i \infty}^{\pi/2 - i \infty} \exp[i m \...
7
votes
4answers
490 views

How to find a tangent line with 2 points of tangency for a curve?

Say I have a function like this: f[x_] := 4 x^4 - 9 x^3 - x^2 + 10; Plot[f[x], {x, -1, 2}] It's obvious that there's a tangent line with 2 points of tangency ...
0
votes
0answers
27 views

Jackson integral applied to a recursion

Two days ago I asked a question about the way to compute a Jackson integral $\int_0^t h(x[s]) d_qs$. But now, I must applied it in the follwing recursion : $ \left\{\begin{array}{l} x_0[t,q] = f[t]\\...
0
votes
1answer
45 views

Dependency of parameter to find maximum vanishes after simplification

EDIT: It turns out I just made a dumb mistake: Simplify[Exp[x^2]*2^n*Pi*D[maxdist[n,x]/n*(1+Erf[x/Sqrt[2]])^(2-n),x]] A portion of my "factor" is actually inside ...