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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16
votes
2answers
807 views

Bug in mathematica analytic integration?

I found Mathematica provides me a wrong answer for a relatively simple analytically solvable integral: ...
11
votes
3answers
409 views

Determine frequency of oscillations

I am wondering how I could determine the frequency of oscillations of a differential model equation? How could I find the frequency from this example given in Mathematica Documentation: ...
1
vote
1answer
73 views

Two graphs in the same plot [closed]

I have the following plots for two graphs: ...
2
votes
3answers
82 views

Converting HeavisideTheta[]s and Sign[]s functions to a single Piecewise[]

I have the product of some Heaviside functions or sign functions, a simple example could be: HeavisideTheta[q^2 - 4]*Sign[q - 3] Another slightly more ...
7
votes
1answer
623 views

Is Mathematica really getting this limit wrong?

I'm trying to calculate: $$ \lim_{\beta \to \infty} \tanh \left( \beta A \right) = \mathrm{sgn} \left( A \right) $$ for $A \in \mathbb{R}$, $\mathrm{sgn} \left( \# \right)$ being the sign function. ...
0
votes
0answers
73 views

A power series expansion

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 $n \in \mathbb{Z}$ and ...
0
votes
1answer
91 views

About doing an sum

I want to explain this summation to Mathematica, For $a >0$ define $n_u, n_d \in \mathbb{Z}$ such that if $\{ a \} \leq 0.5$ then $n_u = [a]-1$ and $n_d = - [a]$ and if $\{ a \} > 0.5$ then ...
6
votes
1answer
109 views

Is it possible to circumvent a bug inside SeriesCoefficient?

As far as I can tell, there seems to be a bug in SeriesCoefficient: ...
2
votes
1answer
82 views

Prove (or check) an expression is positive given constraints on variables?

I'm trying to figure out whether an expression is always positive given positive parameters. When the expression is complicated, I can't do this by eye. Is there any way to make Mathematica prove ...
1
vote
0answers
110 views

Derivative of the Absolute Value Function in Mathematica looks very different from the actual answer

Derivative of the Abs Function in Mathematica looks very different than the actual answer. Why? How to correct this? For example I entered ...
0
votes
1answer
123 views

Computing the volume and the curved surface area

I'm trying to compute this function $y=\frac{1}{2}e^x+\frac{1}{12}e^{-3x}$ to get the volume of the solid of revolution when the area under the curve is revolved once around the x axis. And than get ...
0
votes
1answer
67 views

How to the take derivatives of a parametric function? [closed]

I have a parametric curve of the form $x(t)=2t^3+3t^2-12t,\ y(t)=2t^3+3t^2+1$ How do I take the derivative of that function in Mathematica? Is there a certain function I should use?
0
votes
0answers
67 views

About how Mathematica understands the branchcuts of the complex logarithm [Part 3]

One understands that for the function $\log(z^2+a^2)$ Mathematica implicitly puts the branch cuts to be starting at $\pm ia$ and going up/down respectively on the imaginary axis. The phase of this ...
4
votes
1answer
84 views

When to use GenerateConditions -> True

Many functions, usuallly those involving integration, take a GenerateConditions option which often defaults to False, or at ...
2
votes
1answer
160 views

Integrate does not accept my integrand expression

I want to calculate the symbolic integral, but I could not obtain the final results from Mathematica. ...
1
vote
2answers
141 views

Making mathematica do regulated integrals

Consider the integration, $\int _0 ^\infty dx\ x \tanh( \pi x) \sqrt {x^2 + a^2 } $ where $a$ is a real number. This integral is divergent. We note that an asymptotic expansion of the integrand ...
0
votes
0answers
47 views

problem solving a simple integral equation

I'm looking for a function q(x) so that integral( q(t) , t , x, x+2*pi/3) == a*sin(x)+b Could anyone help me on this one? Thx in advance
0
votes
0answers
58 views

Computing residues of matrix valued functions symbolically

I have a somewhat specific application in mind, but I've run into this kind of problem a few times and never found an elegant solution. Is there an efficient way to get Mathematica to recognize that ...
3
votes
2answers
228 views

How can I calculate the limit without using the L'Hopital's rule

I need to prove this limit without using the L'Hopital's rule: $$\lim_{x\to 0} \frac{(1+a\,x)^{1/4} - (1+b\,x)^{1/4}}{x} = \frac{a-b}{4}$$ How can I do it in Mathematica?
1
vote
2answers
71 views

Integrating a half-normal pdf

The pdf of a half normal distribution is: $\frac{\sqrt{2}}{\sigma\sqrt{\pi}}\exp\left(-\frac{x^2}{2\sigma^2}\right)$, $x>0$ ...
1
vote
1answer
73 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 ...
0
votes
0answers
52 views

Derivative of generating function (Example from documentation)

In the documentation for GeneratingFunction, the following example is given under Examples -> Properties & Relations -> Derivative: ...
3
votes
1answer
80 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
95 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
50 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: ...
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 ...
1
vote
1answer
209 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 ...
6
votes
0answers
145 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 ...
6
votes
1answer
360 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 ...
0
votes
0answers
71 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 ...
0
votes
1answer
69 views

How to evaluate an integral involving normal distribution [closed]

I want to compute the following integral, in which 5 can be replaced by any natural number. But I found Mathematica keep running forever and cannot evaluate it. I want to ask for some help. ...
1
vote
3answers
103 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 ...
0
votes
1answer
134 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
46 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 ...
2
votes
1answer
298 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. ...
0
votes
1answer
93 views

Evaluate integral of a series

I want to evaluate this integral, but it won't work. Does anyone knows why? ...
1
vote
2answers
78 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 ...
4
votes
1answer
183 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
0answers
56 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
42 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
92 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
53 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
160 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 ...
1
vote
1answer
118 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
124 views

How to numerically integrate this integral?

I want to integrate the function funcin (spherical coordinates). ...
18
votes
0answers
195 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: ...
1
vote
1answer
76 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 ...
3
votes
1answer
82 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 ...
0
votes
3answers
248 views

Solving an Integral Numerically

I have been trying to solve the integral equation below, but cant seem to find a way out of this. Can someone please help me out with suggestion? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
1
vote
1answer
72 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 $0$. ...