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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1answer
102 views

Evaluate integral of a series

I want to evaluate this integral, but it won't work. Does anyone knows why? ...
2
votes
1answer
678 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
0answers
153 views

Calculating derivatives of roots of equation

I am interested in calculating how the roots of an equation change as one of the variables does, when the equation is evaluated numerically rather than symbolically. I have edited this code to be ...
1
vote
2answers
129 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
243 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
74 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 ...
1
vote
0answers
267 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
60 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
214 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
233 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
318 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 ...
1
vote
1answer
106 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 ...
26
votes
0answers
374 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
121 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
103 views
1
vote
1answer
82 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
208 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
299 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
365 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 ...
4
votes
1answer
903 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
70 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 ...
5
votes
1answer
200 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
256 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
185 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 ...
0
votes
1answer
66 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 ...
9
votes
3answers
737 views

Inverting a function in a certain region

InverseFunction works well for globally invertible functions, like f = 2*# + 2 &; InverseFunction[f] ...
-6
votes
1answer
142 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?
0
votes
0answers
99 views

Exponential function Integral

I have tried to solve this integral: Integrate[E^(-((a^2 b c^2)/(a^2 + b)))/(a^2 + b)^2,a] Mathemathica is not able to solve it, I have tried the integration by ...
1
vote
2answers
83 views

Unknown limit of an array of area integrals

Could someone explain why Mathematica can't finish computing this limit (this is a limit of an array, when n -> Infinity (n ...
1
vote
1answer
120 views

Improper mutiple integral

I would like to solve the following integral: ...
0
votes
3answers
143 views

How to remove the 1. when differentiating 0.5x^2

My question is very basic, When using the Differentiate functionality of Mathematica in this way: D[0.5 x^2, x] This results in: ...
2
votes
2answers
210 views

Another fractional part related question

Having known the fact that the evaluation of the integrals containing fractional parts often contains errors, I wonder if the integral below possibly evaluates to $0.7$ or this is just a coincidence ...
5
votes
4answers
1k views

How to find the sum all even numbers of this sequence?

I have a sequence $(u_{n})$ $$u_1= 1, \quad u_2 = 2, \quad u_3 = 3, \quad u_{n}= -u_{n-3} + 3u _{n-2} +2 u_{n-1}, \quad \forall n \geqslant 4.$$ I want to list the first $20$ terms of this sequence ...
1
vote
1answer
306 views

Calculating electrostatic potential from arbitrary charge density

In electrostatics, one often desires to know the electrostatic potential generated from the outside of a charge distribution; however, I am interested in finding the electrostatic potential inside of ...
0
votes
0answers
72 views

PDE syntax question

I am trying to solve a PDE of a reaction diffusion equation, and while I'm getting a decent looking solution, I am also getting inconsistent BC / initial conditions warnings and wanted to check if my ...
1
vote
1answer
123 views

Help with finding solution for utility function [closed]

I'm brand new to Mathematica and having trouble finding a solution for Lh based on the first order condition. I'm not sure if it is something I'm doing in Mathematica or something wrong with the ...
4
votes
2answers
400 views

Using units and piecewise functions in Integrate

For simple cases, Quantities appear to be handled well by Integrate: ...
0
votes
1answer
176 views

Revolving the area between two functions about an axis

I'm trying to graph the revolution of the area between two functions about an axis, but I'm new to Mathematica, and not sure how to proceed. My area is defined by ...
1
vote
1answer
297 views

Asymptotic Rate of Growth

How can I calculate the Asymptotic Rate of growth of a function, for instance like: $X^3 - X^2 - X -1$ EDIT: For instance, as you can see in this graph, after the 1200 the function approximates to ...
0
votes
2answers
560 views

Using Mathematica to find poles of Gamma functions

I am concerned about the expression on the RHS of equation A.5 (page 19) in this paper: $$\int\frac{d^d ...
0
votes
1answer
44 views

Showing result of derivative and other functions [closed]

I have a problem with my Mathematica 7.0 When I write: Derivative[x^2, x] Mathematica returns as result : ...
0
votes
1answer
63 views

Different integral when used with assumptions

I want to calculate an integral, but Mathematica gives me different results if I am more specific with the Assumptions option of ...
5
votes
2answers
226 views

Triple fractional part-related integral

The evaluation with Maple suggests the triple integral is around $1$, but Mathematica tells it's $0.0958758$. When using the code ...
6
votes
1answer
179 views

Working with a system of differential equations that cannot be solved explicitly

I have to work a lot with three functions $\;o_1(t), o_2(t), o_3(t)\;$ that are solutions to the certain system of differential equations: ...
2
votes
2answers
225 views

Triple series - evaluation delayed

Trying to figure out if the infinite triple series has a nice closed form. It seems Mathematica is unable to help us here. Numerically, things remain the same, no response. Could you help? ...
4
votes
2answers
134 views
4
votes
2answers
135 views

Integrating a BesselJ integrand to obtain the same result as Maple 16

I would like to check the following integration: Integrate[y*Integrate[1/x*BesselJ[1,x*Exp[I*π/4]]*BesselJ[1,x*Exp[-I*π/4]],{x,0,y}],{y,0,r}] Mathematica 9.0 is ...
1
vote
1answer
199 views

Integral over squared Hermite polynomial

I would like to calculate the uncertainty of the nth Eigenstate of a 1-dim harmonic oscillator. To obtain the result I have to solve the integral $$\int_{-\infty}^{\infty} \psi^* x^2 \psi \:dx$$ ...
3
votes
2answers
344 views

Incorrect value of infinite sum

Wolfram Alpha and Mathematica give an incorrect result (numerically) for the following infinite sum: ...