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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88 views

Help wanted in evaluating an integral

Trying to evaluate an integral. To be specific, I'm trying to find the expectation value of $x^2$ for the ground state of hydrogen. Here is the code I used: ...
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525 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 ...
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80 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 ...
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286 views

Limit of sequence

I tried to calculate the following limit $$\lim_{n\to\infty}n\sin(2\pi en!)$$ Mathematica gets ...
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159 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 ...
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124 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 ...
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99 views

Help with Integrals (and conditional expectations) of the Beta distribution: Integrate[e^(az) z^a (1-z)^b, {z, 0, 1}]

I have a Beta distribution, and am interested in calculating expectations and conditional expectations. The domain on the distribution is $z \in [0,1]$ Ignoring constants of proportionality, the ...
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221 views

Positive integrand giving negative answer

I'm integrating a positive function f(t) times sin(t) from 0 to pi/5 and get -38. Actually f is slightly negative for a short time (smallest value ~ -0.0005), but far from enough to explain this. ...
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445 views

Cauchy principal value integral of a list of numbers. How?

I have a list of numbers that are numerical samples of a function for which I need to find the Cauchy principal value integral. I thought I should be able to combine Interpolation with Integrate to do ...
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807 views

Calculating the mean curvature of a surface - suggestions

I am attempting to calculate the mean curvature [1, 2] of a surface defined by a function of x and y. My function is rather ...
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190 views

How to move differentation before the integral?

I have quite a lot expressions that need to be integrated after switching the integral sign with differentation operator. The additional problem is that the bounds are dependent to one of the ...
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20 views

Issue with Differentiation over a tensor

I am new user in Mathematica. I am working with liquid crystal theory, and one of the notation there is the tensor: $ \Pi_{ij} = \frac {\partial {F_{el}}} { \partial ( \partial {n_i} / \partial { ...
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57 views

Formally invert a $C^\infty$ diffeomorphism

I'm having a problem with a calculation. Starting with $f: \mathbb R^2 \to \mathbb R^2$ having an invertible gradient, I want to compute $\nabla^2(g \circ f^{-1})$. While I know $f$ and $\nabla f$ ...
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63 views

Clairaut's Theorem

Clairaut's Theorem: Suppose $f$ is defined on a disk D that contains the point $(a,b)$. If the functions $f_{xy}$ and $f_{yx}$ are both continuous on D, then $$f_{xy}(a,b)=f_{yx}(a,b).$$ Now, check ...
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46 views

Bounds of a closed curve

how to find the rectangular bounds of a curve which is of the form f(x,y) and forms a closed loop. The sides of the rectangle are parallel to the axes and are tangents to the curve. The time taken for ...
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56 views

PolyLog does not simplify

How come mathematica can not simplify a simple expression involving the PolyLog function? An example is: You know that ...
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48 views

Sharp Ratio Maximization, Closed Forms

I am trying to get a closed form for the following first order conditions (n=4): Here's the nb-File. The code is as follows: ...
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49 views

NIntegrate unexpectedly returns complex number

I am attempting to visualise the effect of shift parameter $\gamma$ on the 3-parameter log-normal distribution. $$pdf(x;\mu,\sigma,\gamma) = ...
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18 views

Not Simplify automatic some expression(values)

I try to calculate $$\text{res}\left(h(z) (\psi ^{(0)}(z)+\gamma )^2,\{z,-4\}\right)$$ the result is $$\frac{1}{6} \left(6 h'(-4)-25 h(-4)\right)$$ the result it is possible to write as $$2 \left(6 ...
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28 views

Does a very large prefactor affect NIntegration time when plotting the result?

I'm using ListPlot[ NIntegrate[f[x,#],{x,a,b}]&/@Range[10,100] ] to plot the integral of the two variable function f as a ...
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66 views

Using Manipulate to determine intersection of two surfaces

Here is what I have done thus far: ...
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39 views

Integration problem: lrgexp

I want to calculate the following integration but it gives the error PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD. The code is: ...
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65 views
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97 views
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48 views

Multidimensional integration does not work

I am trying to solve an integral over Cubic Birillioun Zone, but after taking a long time Mathematica give nothing in return and just repeating the integral form, here is my integral, ...
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65 views

Integration is unevaluated analytically after a variable removed

I am using Mathematica 9.0 to do a symbolic integration as follows: ...
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36 views

Computing integral involving derivatives

I want to evaluate an expression $\int_C g(\nabla f)ds$. This is an integration along a curve $C$ in a plane given as a function of some parameter $s$: ...
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52 views

numerical integration with parameter

Now I'm trying to integrate a function numerically. But it shows always an error message. x=y is not a valid limit of integration I know that this function ...
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94 views

How can I verify double integral solution?

I have a double integral as follows \begin{equation} 1-(\int_0^\infty (\frac{Cje\cdot Cte \cdot e^{\frac{-w}{Cte}}}{(Cte+Cje \cdot w)^2} + \frac{e^{\frac{-w}{Cte}}}{(Cte+Cje \cdot w)}) ...
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95 views

Fourier Transformation of a List

As we know the FourierTransform goes a function of t ,for example, f[t] to ...
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75 views

Piecewise functions Integration with symbol

I want to integrate one piecewise functions as following, ...
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106 views

Boundary value problem: complicated functionals

I am trying to solve a non-linear boundary value problem where the differential equation is a convoluted function of the variable I am trying to solve for. I have attached the code defining the ...
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66 views

Can Mathematica do this integral over $\mathbb{R}^n$?

I have the following function: $$\phi_{k,n,r}: \mathbb{R}^n \rightarrow \mathbb{R}, (x_1,…,x_n)\mapsto (1-r^{n-k}e^{\sum_{i<k}x_i})e^{\sum_{i<j}x_i-x_j}e^{(2-n)\sum_i x_i}$$. Is there any way ...
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107 views

Mathematica Integrate implicit assumptions returns a function not defined in some points while NIntegrate performs integration safely

Hi guys i'm performing a standard integration with mathematica routine Integrate, the function i'm integrating is the following: ...
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51 views

Custom simplification of symbolic definite integral with regards to bounds

I would like to rewrite symbolic definite integrals such that the bounds are always positive. For example : $\int_{-\infty}^\infty f(x) \mathrm{d} x \rightarrow \int_0^\infty \left[ f(x) + f(-x) ...
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27 views

different values of integral with/without bogus assumptions

I do not understand why I get different answers for the following two identical integrals. ...
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63 views

Getting long complex-valued integrals when simpler real-valued expressions exist

I have a long list of real-valued functions I'd like to integrate symbolically. For many of them, Mathematica gives me results with long complex-valued expressions involving weird functions such as ...
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107 views

Complex Convolution

I am attempting to integrate a convolution variable using the following code. However, the program is taking too long to complete the integration. Does anybody have any coding tips that may make ...
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72 views

Computing integrals with differential operator

I've to compute this expression $$ \hat{H} = \frac{1}{4}g_2\int d^3R\int d^3r\ \bar{\Psi}(\vec{R}+\frac{\vec{r}}{2})\bar{\Psi}(\vec{R}-\frac{\vec{r}}{2})\left[ \delta(\vec{r})\nabla_{\vec{r}}^2 ...
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138 views

Complex integrals and residues

I have a question. I try to integrate this function: Integrate[Exp[I k z]*Exp[-Sqrt[k^2 - A^2]x]*Exp[-k^2*L^2/4]/Sqrt[k^2 - A^2], {k, -Infinity, -A}] But ...
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160 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 ...
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84 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 ...
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55 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
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59 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 ...
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83 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 ...
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105 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 ...
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76 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 ...
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89 views

Symbolic representation of bessel series derivative

I want to get symbolic expression for BesselJ derivative, where BesselJ is represented as series: ...
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155 views