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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0
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32 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
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2answers
118 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. ...
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0answers
27 views

How to remove a hold from a result obtained by equating a partial derivative to 0? [on hold]

I have a function g(x,y). I want to set its partial derivative by $y$ equal to 0, obtain an expression depending on $x$ and use it in further calculations. However, the code I am using puts a hold on ...
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0answers
30 views

differentiating an integral [on hold]

I am new to Mathematica. i hope to have the software next week so please excuse the unusual syntax. p(y) means p is a function of y. u(p) means u is a function of p . p(x) is the value of p when y=x ...
5
votes
3answers
244 views

Complex limit gives wrong answer

I'm evaluating $$\lim_{z\to e^{i \pi/2 n}} \frac{z-e^{i \pi/2 n}}{z^{2 n}+1}$$ with Mathematica 9.0.1: ...
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0answers
56 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
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0answers
62 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 ...
2
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0answers
67 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) + ...
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1answer
60 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
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0answers
33 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 ...
10
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0answers
130 views

Strange behaviour of integrals with Cos, Sin, and Exp

During the study of the problem How to solve this integration? I have discovered a strange behaviour of some integrals. I would consider it a bug. ...
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2answers
99 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 ...
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2answers
82 views

Jump boundary conditions

I'm having the following issue that can not find a solution , by using this boundary condition ...
2
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1answer
40 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 ...
5
votes
1answer
121 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 ...
1
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0answers
232 views

A power series expansion [closed]

Consider the function, $f(z) = z\, \tanh(\pi z) \log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ ...
0
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0answers
25 views

Is there a way to save the output from integrate as a function? [closed]

Is there a way I can save the result of my integration as a function? I would like to be able to assign the result of this integration to a function which accepts ...
0
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2answers
125 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 $x=10$? ...
1
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1answer
65 views

Inconsistent Integrate behavior?

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

Construct certain univariate functions over bounded interval having given set of moments [migrated]

We have a class of probability distributions (parameterized by $\alpha =\frac{1}{2},1,\frac{3}{2},2,\ldots$) over the interval $[-2^{-12} \cdot 3^{-3},2^{-16}]$ having as their $n$-th moments ...
0
votes
1answer
356 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
5
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1answer
70 views

ComplexInfinity for a convergent product

The infinite product involving the ratio of (n^2)! to its Stirling approximation ...
0
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0answers
32 views

Inverse Fourier Transform [migrated]

I have to calculate the following Inverse Fourier-Transform, which describe the potential function for a point force on a half-space: ...
3
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2answers
90 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: ...
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1answer
134 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 ...
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2answers
48 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 ...
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0answers
28 views
-1
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0answers
62 views

Plotting points with Euler's Method [closed]

I have the solution for this diff. eq. graphed and assigned to a variable, how do I show points on or off the graph? (dy/dx)=(y^2)-(x^2) It's solution is a Bassel Function conglomeration. Now ...
0
votes
2answers
147 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
277 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
72 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
94 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
52 views

Dirac delta in integrals

I am trying to simplify the following integral ...
5
votes
2answers
136 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
52 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
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1answer
95 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 $m=-1$, ...
1
vote
1answer
52 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 ...
5
votes
4answers
239 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 ...
6
votes
2answers
158 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
2answers
95 views

How to convolve the unit box function and the modified Bessel function of the second kind in 2D?

In 1D the convolution of the unit box function and the modified Bessel function of the second kind $K_0(x)$ works very well. ...
1
vote
1answer
34 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
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1answer
138 views

Solving integral

How can I solve this integral: Integrate[expression, x] where expression is: ...
2
votes
2answers
114 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 ...
0
votes
0answers
63 views

Graphical Representation of Derivatives [migrated]

We know that the derivative function takes as its input a function and gives out another one. The output function is the rate of change of the input function wrt the independent variable which changes ...
10
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1answer
427 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
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2answers
233 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 ...
1
vote
1answer
60 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
205 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
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1answer
98 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
444 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?