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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3answers
321 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
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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
193 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 ...
0
votes
1answer
102 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
2answers
116 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 ...
6
votes
2answers
175 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
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1answer
54 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
115 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
181 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. ...
4
votes
1answer
641 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 ...
3
votes
1answer
99 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
165 views

Is it possible to give the closed-form of the stiffness matrix of triangular prism element?

Suppose the vertices of triangular prism are 1, 2, 3 (bottom triangle), 4, 5, 6 (top triangle), the coordinates of the vertices are $$ (x_i, y_i, z_i), i=1,2,3,4,5,6. $$ We can write the stiffness ...
1
vote
1answer
174 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 ...
10
votes
2answers
282 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 ...
1
vote
1answer
155 views

I want change gamma function form into beta function form

I want to integrate below form ...
0
votes
1answer
63 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 ...
4
votes
3answers
256 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 ...
1
vote
1answer
214 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. ...
-6
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1answer
130 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
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0answers
73 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 ...
0
votes
0answers
92 views

Convergence problems with numerical integration of specific functions

I want to numerically integrate two functions that have several poles inside the integration region. These are the functions: ...
1
vote
2answers
77 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
113 views

Improper mutiple integral

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

Cannot calculate an integral

I am new to Mathematica. So I just run a basic procedure but Mathematica didn't calculate this integral. Maybe it is too complicated to be done. ...
7
votes
2answers
402 views

Double integral over a parallelogram

Problem: Evaluate the following double integral $$\int \!\!\! \int_D (14 x^2+61 xy+42 y^2)^{3} \, dxdy$$ where $D$ is a parallelogram between these four lines: $2x+7y=6$, $2x+7 y=-6$, $7x+6 y=6$ and ...
3
votes
1answer
295 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? ...
0
votes
3answers
111 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
182 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 ...
1
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1answer
230 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
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0answers
63 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
107 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 ...
0
votes
1answer
127 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 ...
4
votes
2answers
326 views

Using units and piecewise functions in Integrate

For simple cases, Quantities appear to be handled well by Integrate: ...
0
votes
1answer
43 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
2answers
150 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; ...
0
votes
1answer
62 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
199 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 ...
5
votes
1answer
164 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: ...
1
vote
1answer
153 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 $$\int_{-\infty}^{\infty} \psi^* x^2 \psi \:dx$$ ...
0
votes
1answer
73 views
3
votes
2answers
143 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: ...
3
votes
2answers
303 views

Incorrect value of infinite sum

Wolfram Alpha and Mathematica give an incorrect result (numerically) for the following infinite sum: ...
2
votes
2answers
198 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? ...
7
votes
4answers
1k views

How to plot and find the volume of a solid?

How to plot and find the volume of the solid enclosed between the paraboloid z=5(x^2+y^2) and z=6-7x^2-y^2 And the answer of ...
4
votes
2answers
99 views

Limit won't compute

Does anyone know why the limit: ...
10
votes
4answers
264 views

No response to an infinite limit

Trying to compute this limit, things seem to get frozen, even for hours. What would you recommend to fastly compute it? ...
0
votes
0answers
77 views

Algebraic condition from a non linear equation

I have got a system of equations which look like this: $\theta_{1}^{2}e^{\phi_{1}\cos(\Omega z)}\tilde{w}\cos^{2}(\theta_{1}\sin\Omega z)\sin^{2}\Omega z+\frac{1-\lambda\cos(2\theta_{1}\sin\Omega ...
1
vote
1answer
874 views

How to find the area between two curves

Find the area between y = 1 - x/π and y = Sin[x]. Here is what I have typed in so far into Mathematica: ...
9
votes
2answers
555 views

Problem with numerical evaluation of analytically solved integral, solution way off

The following command in Version 9.0.1: N[Integrate[x^50*Sin[x], {x, 0, 1}]] gives $1.4615\times 10^{48}$ which is way off from the correct solution which is ...
2
votes
1answer
168 views

How can I get the limit of a certain infinite product?

A first look at it suggests the fact the limit is precisely $1$. To check that I tried Mathematica, but no output so far. Most probably it converges very slowly. Is there any way to get the limit? ...