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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5
votes
2answers
290 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
271 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
102 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
171 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
vote
1answer
190 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
59 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
96 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
106 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
230 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
125 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
59 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
187 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 ...
2
votes
1answer
137 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
132 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
70 views
3
votes
2answers
135 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
281 views

Incorrect value of infinite sum

Wolfram Alpha and Mathematica give an incorrect result (numerically) for the following infinite sum: ...
2
votes
2answers
190 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? ...
6
votes
4answers
774 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
89 views

Limit won't compute

Does anyone know why the limit: ...
9
votes
4answers
253 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
69 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
600 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
486 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
160 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? ...
5
votes
1answer
200 views

Prove an identity in quantum harmonic oscillator

Problem: In the context of quantum harmonic oscillator the eigenfunctions are given by: $ u_n(x) = (N_n/\sqrt{b}) H_n(x/b) \exp\left[-x^2/(2b^2)\right] $, where $N_n$ is the normalization factor: $ ...
1
vote
1answer
117 views

Function derivatives in arbitrary dimension

I have a higher dimensional function: $$f(x,t)=-\ln(t)-\ln(1-\left\|x\right\|^2-t^2)$$ where $x\in\mathbb{R}^n,~t\in\mathbb{R}$. I want to compute the derivatives with the commands ...
0
votes
1answer
149 views

Does Mathematica know if an integral is convergent or not?

Consider the following integrals that I asked Mathematica to do, ...
9
votes
3answers
537 views

Different results for integration using Mathematica and MATLAB

I have the following integration: $$\text{y}=2 \sqrt{\frac{1}{\pi }} \int_0^{\infty } \frac{e^{-z} \left(1-e^{-\frac{z}{b}} \left(\frac{a}{a+c z}\right)^L\right)}{\sqrt{z}} \, dz$$ I get different ...
0
votes
1answer
93 views
8
votes
3answers
208 views

Pulling constants out of integrations [duplicate]

The following is the code and output of a Mathematica command How do I get Mathematica to remove $g(y)$ outside the integral?
6
votes
1answer
76 views

Is it possible to find a function from first few terms in the expansion

Is it possible to find a function if first few terms of the expansion is known. For example if I have this series $f(x)=\frac{k^3 x^2}{6}-\frac{k^5 x^4}{120}+\frac{k^7 x^6}{5040}-\frac{k^9 ...
4
votes
2answers
124 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 ...
4
votes
2answers
173 views

Can Mathematica (or its extensions) do integration following Risch algorithm?

I wonder whether there are option for indefinite integration in Mathematica that alow to choose the algorithm? Is there an option to use this algorithm in Mathematica?
4
votes
1answer
139 views

Volume within parameter space

Imagine a parameter space with variable 0<p<1, 0<e1<1/2 and 0<e2<1/2. ...
0
votes
1answer
106 views

Explicit, closed formula for recursive integral as a function of the recursive parameter

This is a follow-up of this question/answer. I'm working on a recursive integral more complicated than the one on the linked question, but this one can be used as an example. I would like to obtain ...
2
votes
1answer
83 views

Integrate and ConditionalExpression Output

I am integrating some difficult functions and using the conditional output to place bounds on parameters to ensure integrability, but it seems that not all of the conditions are being returned. The ...
0
votes
0answers
54 views

limit calculation step by step [duplicate]

I calculate such limit with Mathematica: ...
-1
votes
3answers
790 views

How do I determine the maximum value for a polynomial, given a range of x values?

I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
0
votes
1answer
92 views

How can I find the derivative of a combinatorial expression? [closed]

I want to differentiate the following equation: n = (nchoosek)*p*(1 - p)^(n - k) After differentiating my result is: ...
5
votes
0answers
165 views

Strange Integrate behavior (a bug!)

The following two calculations should give the same result. After all, integration is a linear operation. I have pasted the code below in case you want to play with it. ...
3
votes
2answers
311 views

Algorithm for parts integration

Sorry if this is a duplicate, I've searched how to do this to no avail. What I'd like to do is a function that integrates by parts $n$ times, i.e $$ \int u(x) v(x) dx = u ...
3
votes
1answer
310 views

Integral of Lorentzian yields different results depending on when parameter assigments are made

I'm evaluating the integral of a Lorentzian, which I know equals one. First I define the function and evaluate the integral in two slightly different ways. Surprisingly, I do not get the right answer ...
4
votes
2answers
650 views

Paths integrals in the complex plane

I can't find how to calculate path integrals of complex functions in the complex plane. For example: $$\oint_{\mid z \mid =2}\frac{1-e^z+z}{z^3 (z-1)^2}dz$$
12
votes
2answers
763 views

How can I implement the method of Lagrange multipliers to find constrained extrema?

I want to form the function $h=f-\lambda_{1}g_{1}-\lambda_{2}g_{2}$ where $f$ is the function to optimize subject to the constraints $g_{1}=0$ and $g_{2}=0$ so that I can solve the first partial ...
2
votes
2answers
193 views

Calculate information entropy integral in infinite square well problem

In the context of information theory, entropy is a measure of uncertainty of a random variable. In quantum mechanics, the uncertainty principle states that $\Delta x\Delta k \ge 1/2$. The same can be ...
5
votes
3answers
199 views

Calculate integral for arbitrary parameter n in infinite square well problem

I'm continuing[1,2] the study of an infinite square well in the context of quantum mechanics. Ultimate goal is to calculate the product $\Delta x\Delta k$, for various eigenstates, that is for ...
0
votes
0answers
52 views

Reducing a long complex expression to a simplier one by using assumptions

so I have an ugly looking equation that I wish to solve under some specific circumstances. Using DSolve I write; ...
4
votes
1answer
171 views

How do I compute the entropy of the beta distribution?

I tried Expectation[-q*Log[q], q \[Distributed] BetaDistribution[a, b]] and got ...