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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3
votes
1answer
105 views

Integration over a convex combination of a region: $\int_{\Omega} (w_1 z_1 + w_2 z_2)^{1-\sigma} d (z_1, z_2)$ where $\Omega = \{ z_1 + z_2 = 1\}$

Take $w,z\in R^{n}$. I am interested in integrating (as generically if possible) $$\int_{\Omega}(w \cdot z)^{1-\sigma} d z$$ Where the domain of $\Omega$ is $1$ dimension, and includes the convex ...
1
vote
0answers
95 views

Simple Jacobians, Gradients, etc. with arbitrary length vectors/matrices?

Is there any way (or a package built for it) can do simple operations with vectors and matricies of arbitrary size, but conforming extents? For the simplest example to test, given an arbitrary vector ...
6
votes
0answers
150 views

Incorrect evaluation for Thue-Morse signed harmonic series

I would like to evaluate $$s = 1 - \frac{1}{2} - \frac{1}{3} + \frac{1}{4} - \frac{1}{5} + \frac{1}{6}+\frac{1}{7}-\frac{1}{8} - ... + \frac{(-1)^{\textrm{binary digit sum}(n-1)}}{n} + ... $$ where ...
1
vote
1answer
79 views

RegionPlot of a Double integration [closed]

Hey guys I have a problem where I want to sketch the region of integration: Integrate[x Cos[y^2], {x, 0, 3}, {y, x^2, 9}] I know I have to use ...
14
votes
1answer
330 views

How to represent a continuous monotonic phase of Airy functions?

Note: In this question I am concerned only with real-valued variables and functions. DLMF, §9.8 Airy Functions, Modulus and Phase, formula $9.8.4$ defines the phase of Airy functions: ...
3
votes
1answer
84 views

Why does Mathematica list the variables in a double integral backwards? [closed]

I am an advanced novice Mathematica user and have done a fair amount of single-variable calculus things with it. This semester I am using Mathematica for multi-variate calculus and when I tried to ...
1
vote
2answers
101 views

Using Mathematica to derive the PDF of the normal distribution

I am trying to use Mathematica, in this case in a well known and rather simple list of equations, but I get stuck whit Mathematica. Since I am just starting to use Mathematica for mathematical ...
0
votes
1answer
57 views

NIntegrate and NumericQ [closed]

I need to do numerical integration --> differentiation --> numerical integration. I tried to apply the technique described in the accepted answer to a similar question: ...
1
vote
1answer
227 views

How do I get all possible solutions in an underdetermined system? [duplicate]

I have two problems which I'd like to solve with Mathematica. If I have a system of two equations with three unknowns, how can I get to list all possible solutions for the unknowns? Here is what I ...
0
votes
0answers
30 views

Is it possible to obtain vector differentiation results in terms of vectors rather than components? [duplicate]

When doing certain operations on vectors in Mathematica it is quite desirable to convert the results back into coordinate-free notation. Unfortunately, after going through the Documentation Center and ...
6
votes
1answer
365 views

What is the mathematical meaning behind D[f]?

y = a + b x; I can understand this output of the ordinary differentiation of y w.r.t. x ...
12
votes
2answers
3k views

How to calculate contour integrals with Mathematica?

How to calculate the integral of $\frac{1}{\sqrt{4 z^2 + 4 z + 3}}$ over the unit circle counterclockwise for each branch of the integrand?
0
votes
0answers
89 views

Numerical Differentiation of an interpolated list.

I have a synthetic spectrum with a wavelength range of .3 to .7 microns. I have interpolated this spectrum for re-sampling purposes. However, I am also attempting to calculate the first and second ...
1
vote
3answers
113 views

Area enclosed by two functions

i want to calculate the area percentage of a function in a certain regime above a constant threshold. For example: f[x] = sin[x] x² from 0 to 2 with a threshold ...
4
votes
1answer
215 views

Asymptotic expansion

I wanted to expand a function of $x$ about $x=\infty$ and see its coefficients as a function of the parameters $m,n,q,y$ and I wrote this - but it didn't work! It gave me back a very complicated ...
0
votes
1answer
147 views

Revolve A Function Around the Y axis? [duplicate]

I am seeking to revolve the are between the functions function $d(x) = Exp(x)$ and $e(x) = 4 - x^2$ around the line $x = 2$. I am using RevolutionPlot3D, so I ...
0
votes
0answers
49 views

Errors while computing some terms of the Euler–Maclaurin formula

Here is an issue I came across while I was applying one of the well-known versions of Euler–Maclaurin formula. I try to realize why Mathematica goes wrong with this code below ...
0
votes
1answer
95 views

Evaluate integral of a series

I want to evaluate this integral, but it won't work. Does anyone knows why? ...
2
votes
1answer
531 views

Time derivative of unit vector in spherical coordinates

Is it possible to take a time derivative of a vector given in some curvelinear coordinate system (i.e. spherical)? Mathematica would need to take into account the time dependence of the basis vectors. ...
1
vote
2answers
84 views

A possible error related to the evaluation of a double integral

According to the Mathematica, the integral below NIntegrate[ Log[Log[1/(x y )]] Log[1/(x y )]^(-0.5 - 1), {x, 0, 1}, {y, 0,1}] might possibly evaluate to ...
6
votes
2answers
152 views

Fundamental Theorem of Calculus for definite integrals… assume continuity?

So here's the problem: I can evaluate the indefinite integral: Integrate[D[u[x], x], x] u[x] However, I'd like to ...
0
votes
0answers
59 views

An error message with NIntegrate and inability to plot the integrand

I took a function of x which depended on parameters on m,n,a,y and then first summed up the n from -Infinity to Infinity and then I set the other parameters to some random values and then I asked it ...
0
votes
1answer
43 views

Integral not being evaluated

I'm trying to do the following integral, but Mathematica won't evaluate it - it just spits out the actual symbollic integral (sorry I'm not sure how to copy the output into this post so it appears as ...
1
vote
0answers
102 views

Limit of sequence

I tried to calculate the following limit $$\lim_{n\to\infty}n\sin(2\pi en!)$$ Mathematica gets ...
1
vote
1answer
55 views

Extension of harmonic number to the real domain

What is exactly the domain of validity of the identity: Sum[1/(k + j - 1), {j, 1, i}] == HarmonicNumber[k - 1 + i] - HarmonicNumber[k - 1] when ...
3
votes
1answer
169 views

Convergence in NIntegrate vs Integrate

I am faced with this situation that for a certain integration, $\int _0 ^\infty \frac { \tanh (\pi \sqrt{x} )} {\sqrt{x+10} } dx$ - the command Integrate returns ...
0
votes
2answers
135 views

NDSolve boundary query / Extracting values from solution

I have a function $O_{2}$ with boundary conditions $O_{2}(r_{o}) = p_{o} $ and $O_{2}(g) = O_{2}'(g) = 0$. I plot it using the solver code below; ...
1
vote
1answer
150 views

Can ParametricNDsolve be used for coupled PDEs with 5 parameters?

I have a system of coupled PDEs with five parameters that I only know ranges for rather than explicit values, and I was wondering if I could define a parametric equation with ParametricNDSolve and ...
0
votes
2answers
140 views

How to numerically integrate this integral?

I want to integrate the function funcin (spherical coordinates). ...
1
vote
1answer
79 views

Poor performance when evaluating double integral of hat functions

I am trying to evaluate a double integral but am having performance issues. First a bit of math I am using a Galerkin like scheme to discretize operators in an equation I am working with. The ...
18
votes
0answers
221 views

Are greek symbols causing different evaluation?

I've updated today to Mathematica 9.0.1.0 from version 8 and found something that absolutely confuses me. Let us define a piecewise function: ...
4
votes
2answers
111 views

Inconsistent results for equivalent converging symbolic integrals

I have looked at previous questions and I'm aware that this seems to be a known bug: Mathematica giving inconsistent results for symbolic integrals done in different ways. The origins for the bugs ...
3
votes
1answer
85 views

How to calculate the residue of $1/f(z)$ at a numerical approximation to a root of $f(z)$?

The input Residue[1/DirichletL[19,10,s],{s,s0}] gives 0 even when s0 is a root. For ...
1
vote
1answer
76 views

About an elementary limit

Here we have an elementary limit that Mathematica simply doesn't want to compute it. What solutions might I have to fix that? Could you help here? As you can easily guess, the limit is precisely $0$. ...
3
votes
2answers
174 views

How to find the maximum of this function on the positive real line?

I need to maximize this function on the positive real line: $$ \frac{1}{\Gamma(x)^{14}}\cdot\frac{1}{{\frac{323.6}{14x}}^{14x}}\cdot(1.22578*10^{19})^{x-1}e^{-14x} $$ the correct answer should be ...
4
votes
3answers
248 views

Creating a function with integral zeroes of the 0th, 1st, and 2nd derivatives

I would like to be able to randomly generate functions, each of which satisfies $f : [-10, 10] \rightarrow [-10, 10]$ All the zeroes, critical points, and inflection points have an integral ...
10
votes
2answers
239 views

How to take derivative of parameterized coordinate?

Suppose I have a vector in $\mathbb{R}^n$ but $n$ is not known in advance. I want to be able to write functions which operate on the components of that vector, and then I'd like to be able to take ...
0
votes
1answer
94 views

Mathematica does not solve this integral [closed]

I want to compute the integral of a polynomial in t, which I know an analitical solution exist. But Mathematica give me as result the input, not the result of the integral: I already know this ...
4
votes
1answer
518 views

Is it possible to calculate a Lebesgue integral in Mathematica?

As the title says, I wonder if it is possible to calculate a Lebesgue integral in Mathematica, especially when the domain of integration is $\mathbb{R}^N$, or in other words multivatiate Lebesgue ...
0
votes
1answer
49 views

Excluding an interval of parameters from Integrate [duplicate]

I'd like to compute an integral that depends on a parameter, but I'd like to exclude an interval from the computation. For concreteness, say I want to compute ...
3
votes
2answers
109 views

About the wrong evaluation of an integral

Here is an integral I've been studying in my research and I've just realized that Mathematica $8.0$ is unable to correctly compute it. I have 2 simple questions to ask: $1)$. Is my code below ...
5
votes
1answer
169 views

Simplification of integrals depending on a parameter [duplicate]

Assuming[Element[n, Integers], Integrate[Sin[x]*Sin[n*x],{x,0,Pi}]] returns 0, which is obviously wrong for n=1. ...
1
vote
1answer
136 views

Numerical saddle point problem of a function of many variables

I want to find the following saddle point of the function of 10 variables: . I am not able to find the stationary points by setting the first derivatives to 0, so I need do optimize the function ...
3
votes
1answer
80 views

Problem with limit that requires L'Hôpital's rule to compute

Consider the following limit. Limit[(a - Sqrt[a^2 + x])/(a^2 - a*Sqrt[a^2 - x]), x -> 0, Assumptions -> {a > 0}] Mathematica 9.0.1.0 gives ...
1
vote
1answer
178 views

Error Function Integral (Erf)

Any idea how to solve analytically this integral Integrate[(a Erf[a Sqrt[b/(a^2 + b)] c])/(a^2 + b)^(3/2), a] I tried substitution u=a^2 + b, but it didn't work. ...
1
vote
1answer
150 views
0
votes
1answer
62 views

One more question about Assumptions and Integrate

There are many questions about assumptions here. Many of them are problem specific. That is why I want to ask a question in the most general way. Why does Mathematica solves this ...
8
votes
3answers
563 views

Inverting a function in a certain region

InverseFunction works well for globally invertible functions, like f = 2*# + 2 &; InverseFunction[f] ...
3
votes
1answer
272 views

A Bessel & Struve functions related integral

I try to numerically compute this integral and I don't figure out why on earth Mathematica is not able to do it. Is my input correct? Does it possibly have a closed form? ...
-6
votes
1answer
123 views

Alternative closed forms for digamma expressions

What commands should I use such that Mathematica / W|A express $$\psi(1+i)+\psi(1-i)$$ exclusively in terms of trigonometric functions?