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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131 views

A triple integral involving Abs over an ellipsoidal region

I'm a newbie and I'm trying to calculate a triple integral. But Mathematica doesn't output for half an hour and the CPU occupancy rate of my Wolfram doesn't changed when it's calculating. Here is the ...
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102 views

Solving a functional equation

Suppose I have two functions f[x,y,z] and g[x,y,z], both analytically defined. I want to solve for a function ...
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84 views

Determining the order of continuity (smoothness) of a function

Is there any method to determine the order of continuity of a function (just like an interpolant) over a given domain, or at least determine the continuity on a given order? For example, according to ...
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55 views

Continuous integration of a tensor function using discrete density values

Hei, I am wondering is it possible to implement continuous integration using Integrate() of a fourth order tensor with discrete density values. ...
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46 views

Discrepancy between laplace and fourier transform of gaussian

The function in question is Exp[x^2/2] for x>0 Laplace transform should be the same as the fourier transform since the function is absolutely integrable. Fourier: They are indeed the same ...
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136 views

How can I improve the solution of my PDE?

I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
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58 views

Multiplying two sets of data (x,y values, but different x density) followed by integration of the product

I've been trying to do this by myself today, but no luck yet. Please, see attached image. Basically, I do have two data sets A (x1,y1) and ...
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45 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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440 views

Mathematica can't, or won't evaluate an integral (again)

I'm relatively new to Mathematica and really need some help here to spot what's going wrong with my integration issues; Mathematica doesn't evaluate my integral, after a fair amount of time running, ...
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109 views

Piecewise functions Integration with symbol

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

Derivative with respect to a tensor

I am trying to differentiate a tensor with respect to another one in Mathematica, but I can't do it. Down below is the code I am using: ...
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80 views

Can NIntegrate be used with the Levin method in several dimensions?

I've got some data in the form of an interpolating function. It's a function of three variables, $\rho(x,y,z)$. I'd basically like to integrate this with some phase over a cube of known size, like $$ ...
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114 views

Giving hints to Integrate

I working with the integral ...
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73 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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90 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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851 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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105 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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165 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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133 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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101 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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216 views

Problem with Integrate

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520 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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928 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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23 views

Suddenly error when training SVM

I am running Classify[] function using a SVM model, suddenly I get an amazing error that I can not resolve it here is my code. The data is imported from a file *.txt ...
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45 views

Definite integral evaluation

I want to evaluate the following integral: g[T_] := Integrate[(x^4*Exp[x])/((((A*(x^4) (T^4) a^4)) + (v/L) + (R*T*x)) (((Exp[x] - 1)^2))), {x, 0, (d/T)}] ...
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55 views

Product of two Meijer's Function

I want to evaluate an integral $I_1$ defined in $Eq.(1)$ as \begin{align} I_1=\int_{0}^{\infty}\frac{x\exp(-\beta x)K_1(\alpha x)}{1+x}dx\tag{1} \end{align} Where $\alpha\geq0$, $\beta\geq0$, and ...
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62 views

How to evaluate this integral with a bessel function

I have to evaluate this integral, Sin[θ] 2 π BesselJ[0, k Sin[θ] (μ[j] - μ[i])] Exp[2 k^2 σ^2 Cos[θ]^2], wrt $\theta$ between the interval [0, $\pi$]. The ...
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29 views

How do I numerically integrate the result of NDSolve if it depends on several variables?

I am trying to numerically integrate solution of NDSolve. I am trying to integrate my result of NDsolve in line 97 of my notebook, but am getting the error ...
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15 views

Integration with IntervalMemberQ

I define an interval and its associated index function. ...
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62 views

How to evaluate this integral

I am trying to evaluate the following integral in Mathematica: ...
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33 views

Integration of a Gaussian function in kernel density estimation

I came recently across an odd result of mathematica, which so far I cannot explain. In a standard kernel density estimation (example http://www.ssc.wisc.edu/~bhansen/718/NonParametrics1.pdf) the ...
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68 views

What is the function in Mathematica that can be used to find the derivative of a constant value function with respect to an arbitrary matrix?

I have a function that consists of some matrices. This function results in a constant value. I need to take the partial derivative of this function with respect to one of the matrices it depends on. ...
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65 views

Finding double inverse Laplace transform numerically

Edit: I asked Prof. Valko, he was so nice to point out where the mistake is. The problem is solved ! Thank you for your attention ! Recall the the double Laplace transform of a function $f(x,t)$ is ...
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75 views

Mathematica: Derivative appears to be wrong

I'm first getting f(x) by computing an implicit equation. Then I want to take the derivative. Later on, when I plot both f(x) ...
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0answers
36 views

Error Message: Invalid integration variable or limit(s) in 1

I write the line: Integrate[1/{1 + Sin[2 x]}, x] And gives the error message: Invalid integration variable or limit(s) in 1. No solutions I'm trying work, and other integration problems are working ...
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56 views

Solving this equation with NDSolve

I'm trying to solve a differential equation numerically. I've written this code but it is leading to some errors "initial history needs to be specified for all variables for delay-differential ...
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93 views

Integrate dealing with Sqrt gives wrong answers

I often find when I integrate something with a Sqrt[x] term in it, Mathematica gives an incorrect result. I assume this must be due to some kind of incorrect ...
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37 views

Possibility of an output for this integral

Any clues as to whether an output exists for this expression where t and f are positive real numbers that can be treated as constants ...
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64 views

To calculate the differential of a function

I need to calculate the differential of a function WaveNumber. However, when I compile the code, it generates followig error: Infinite expression 1/0. ...
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40 views

Solving Integral -syntax or interpretation problems

WA interpreter achievement not well this entry from Mathematica, steps need to see the full resolution input WA ...
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58 views

The system can not be solved

I'm trying to solve this equation: f[a_][r_]=((a*r/12)*(1+(r/12))^n)/(((1+(r/12))^n) - 1) When I type Solve[f[a][r]==p, a] ...
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54 views

Partial derivative of recursive exponential $f(x)=\sum^{K_2}_{k_2=1}c_{k_2}\exp(-z^{(2)}_{k2})$ w.r.t. the deepest parameter

I was trying to take the derivative of the following equation (which can be depicted nicely in a tree like structure, look at the end of question for diagram): $$f(x) = f([x_1, ..., x_{N_p}])= ...
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77 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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50 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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87 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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0answers
81 views

Plotting Real and Imaginary parts of Riemann Surfaces

I'm working on a project where I need to take curves like, for example, $y^{2}=(x^{2}-1)(x^{2}-3)$ and plot their real and imaginary parts. More specifically, let $x$ just be real and then plot ...
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52 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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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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79 views

Using Manipulate to determine intersection of two surfaces

Here is what I have done thus far: ...
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51 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: ...