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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1
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2answers
114 views

How to convolve the unit box function and the modified Bessel function of the second kind in 2D?

In 1D the convolution of the unit box function and the modified Bessel function of the second kind $K_0(x)$ works very well. ...
0
votes
0answers
63 views

Switching from Integrate to NIntegrate

I'm trying to decrease the amount of time that it takes to run the following code: ...
1
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3answers
58 views

A function calculating a multiple integral and taking multiplicity as a parameter

I have a function of the following form: $$ \varphi_n(x)= ...
3
votes
1answer
54 views

Integrating a gradient and matching terms automatically

I am trying to integrate a function $\nabla w(x,y)$ indefinitely knowing both components of $\nabla w(x,y)$. I have a function dw[x_,y_] that I have defined. I then ...
0
votes
0answers
77 views

Setting up and solving an equation

I would like to solve the equations: $$ F(\xi;x,t)=\int_0^\xi u_{0}(\xi)\:d\xi+\frac{(x-\xi)^{2}}{2t} $$ to use in evaluating: $$ u(x,t)=\dfrac{\int_{-\infty}^\infty \dfrac{x-\xi}{t} ...
1
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1answer
60 views

How to find the pole of a equation where the residue exist?

I want to calculate the residue of an equation, such as: equ = 1/((x - 2)Sqrt[x - 1]) So first I need to find the pole of the equation. My method is find the ...
2
votes
2answers
116 views

Any reason why this definite integral is so slow to compute and the indefinite fast?

This integral is easy and fast to compute Integrate[Sqrt[(x^2) + k ], x] $$\frac{1}{2} x \sqrt{k+x^2}+\frac{1}{2} k \log \left(\sqrt{k+x^2}+x\right)$$ But ...
0
votes
0answers
33 views

How can I get left-sided-sequence with InverseZTransform

InverseZTransform[z^2/((4 - z)*(z - 1/4)), z, n, Assumptions -> {1/4 < Abs[z] < 4}] (* -(1/15) 4^-n (-1 + 16^(1 + n)) *) the result is not true.It only ...
1
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1answer
118 views

Summing infinite series that converge only for some parameter values

The input Sum[d^t,{t,0,Infinity}] produces output 1/(1-d) which is correct for $|d|<1$. But for $|d|\geq1$ the sum does ...
1
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1answer
32 views

Mathematica Integral[] return [closed]

I am new to mathematica and while trying to find the double integral of 8-xy over -2 ...
1
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2answers
136 views

How to do this integral? [closed]

Is there any workaround to do this integral? Integrate[(x^2+2 x+1+(3 x+1) Sqrt[x+Log[x]])/(x Sqrt[x+Log[x]] (x+Sqrt[x+Log[x]])),x]
0
votes
0answers
132 views

Implicit hidden assumptions of Mathematica with Limit

I've stumbled upon the following symbolic limit (a tricky one): Limit[(Sqrt[2] v)/Sqrt[v^2 - c^2 (1 - 1/c Sqrt[c^2 - v^2])], v -> 0] Mathematica gives 0 as ...
8
votes
0answers
86 views

Slot number cannot be filled

I got a strange message with the derivative of a two-argument function defined by a definite integral. For example if "f" is defined as: ...
2
votes
1answer
82 views

Getting wrong result when Integrating under an assumption [duplicate]

The simple integral $$\int_0^b \cos\left(\frac{2\pi m(y-\eta)}{b}\right) \cos\left(\frac{2\pi \eta}{b}\right)\mathrm{d}\eta$$ can be easily evaluated by Mathematica as, ...
0
votes
0answers
52 views

Using DeleteCases to ignore term of Product

I'd like to calculate $\int_{-\infty}^{\infty}\mathrm{d}x/(1+x^6)$ through a variation of the residue formula, which is $\int_{-\infty}^{\infty}f(x)\mathrm{d}x=2\pi i\sum \text{Res }f$ for Residues in ...
0
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0answers
44 views

Problem with indefinite integral

How do I calculate this integral with mathmatica? integrate[(Exp[-x/a]Exp[-p x/a])/(x^2 (1-(a/t)^2 Exp[-2 x/a])^(1/2)),x] a, p, t are constants
-2
votes
1answer
55 views

Finding unit vectors which makes an angle 60 degrees with both {1, -1, 0} and {1, 0, -1} [closed]

Find unit vectors which makes an angle 60 degrees with both vectors {1, -1, 0} and {1, 0, -1}.
3
votes
1answer
96 views

Indefinite integral of nested trig functions [closed]

I tried vainly to integrate nested trig functions like Integrate[Sin[Cos[x]], x] Mathematica does not find a solution. At first I thought there was no solution, ...
6
votes
1answer
89 views

How correctly use WhenEvent to detect when gradient is over a certain value?

So I wish to stop integrating my PDE when the spatial gradient is larger than some value, let's say 10. That is to say, my WhenEvent condition wants to be stop when the the maximum gradient over all x ...
0
votes
1answer
54 views

Evaluate as much of an integral as possible [closed]

Consider the integrand $\qquad \cos(x+\sin^{-1}(x)) = \sqrt{1-x^2} \cos(x) - x \sin(x)$ If I ask Mathematica to integrate $\cos(x+\sin^{-1}(x))$, Mathematica is unable to do so analytically (due to ...
4
votes
3answers
238 views

How can I plot a paraboloid?

How do I plot a function for a paraboloid? Im putting together surfaces to model lipstick. I need the paraboloid for the top part and then I'll be cutting the paraboloid at angle with another surface. ...
3
votes
1answer
60 views

Evaluating function

I'm trying to evaluate this function, which is gradient of integral with variable limit of integration: $$ u(x,y,t)=\nabla(\int_{v(x,y)}^\infty \frac{e^{-b(t-\tau-c)^2}}{\sqrt{\tau^2-{v(x,y)}^2}} ...
1
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1answer
47 views

Unexpected behavior in symbolic integration with GenerateConditions->False

Consider the following two symbolic integrations: ...
0
votes
1answer
40 views

Limits at infinity not neglecting added constants [closed]

This is such a simple question that I'm sure it must be answered somewhere, but I haven't had any luck finding an answer. I am trying to simplify expressions of the form: $$f(x) = ...
1
vote
0answers
41 views

How obtain the n-th derivative of a function with an implicit variable? [duplicate]

I'm interested in obtain the analytical n-th derivative with respect to the variable $x$ of an implicit function like $V(h(x))$ where $h(x)$ is an implicit equation and can not be obtained the ...
-9
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1answer
77 views

How to partially differentiate tu[t]u'[t] with respect to t [closed]

How can I partially differentiate tu[t]u'[t] with respect to t in Mathematica?
-2
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1answer
64 views

Wolfram Mathematica ONLINE does not give me the solution for the following integral [closed]

I have some problem in Mathematica and I could not evaluate the following integral. There is a closed-form solution for the following. Can someone please give me the result. ...
0
votes
1answer
44 views

Integrating Poisson distributions [closed]

I'm trying to do the following Integrate[Exp[-λ] λ^k/k!, {k, 0, ∞}] The answer should be 1 but Mathematica is unable to do it. Same story when I try the ...
2
votes
2answers
150 views

Revolve a non one-to-one function about the y-axis

I am attempting to revolve $f(x)=-x(x-3)(x-2)^2$ about $x=0$. What I have come up with is that I need to redefine each interval between the relative extrema as a separate function, and then treat it ...
4
votes
1answer
177 views

Computing the Caputo fractional derivative of a polynomial

In fractional calculus, the Caputo derivative of a monomial has the following form: $$\operatorname{\mathit D}_t^\alpha\,t^\beta = \frac{\Gamma(\beta+1)}{\Gamma(\beta-\alpha+1)}t^{\beta-\alpha}$$ I ...
1
vote
1answer
42 views

Having trouble taking derivative of a function and assigning it to a new function [closed]

I am trying to take the derivative of a function and assign it to a different function name, but I am getting an error message (I think). Here is my Mathematica input: ...
0
votes
1answer
80 views

How to evaluate the integral of exponentials

I want to evaluate the following integral wrt $\phi$ from 0 to $2 \pi$: ...
3
votes
1answer
110 views

Mathematica Can Find the Primitive Function But It Cannot Find the Closed Form for Corresponding Definite Integral

Consider the following function f = 1/2 (-3 + 4 u) Sqrt[-u (1 + u) (-1 - u + u^2)] where it is assumed that ...
40
votes
2answers
746 views

Why does Mathematica report that $\int_1^\infty\frac{\sin(\sqrt{x})}{\sqrt{x}}dx$ = $2\cos(1)$?

Bug introduced in 7.0 or earlier and persisting through 10.4 or later Mathematica 10 gives the following very odd result, ...
0
votes
1answer
62 views

Improper Integral Difficulty [closed]

Trying to do the problem $$\int_0^{\infty}e^{-sx}\cosh(ax)\,dx.$$ where we have the assumption that $s>|a|$ and everything is a real number. We tried: ...
0
votes
2answers
87 views

Expression of an integral

I am doing the following integral in Mathematica with $a>0$: $$\iint e^{-\frac{(x_{1}+x_{2}-2b)^2}{4a}}dx_{1}dx_{2}$$ My code is ...
3
votes
2answers
159 views

How to get the training error and the validation error using Classify function with SVM

I am using Classify[] function with Support vector machine model. I need to analyze the quality of results by analyzing the training error and the validation error ...
1
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1answer
46 views

numerical integration errors

I have plotted the following integrals with numerical integration nicely without any error: ...
-3
votes
1answer
108 views

How to symbolically integrate 2D exponential function? [duplicate]

Is it possible to symbolically solve a 2D integral of the following form $$\int d \vec{r}e^{-\frac{\left| \vec{r} - \vec{r}' \right|^2}{2c}}e^{-i \vec{k} \cdot \vec{r}} $$ where $\vec{r} = (x,y)$ and ...
1
vote
1answer
69 views

NIntegrate::inumri: error [closed]

I am getting the following error: NIntegrate::inumri: The integrand c (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- (1+Times[<<2>>])^0.5)) (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- ...
2
votes
2answers
166 views

Symbolic vs numerical integration

This is related to a question that I asked before but didn't resolve quite well. I want to obtain the solution of the following expression analytically: ...
1
vote
0answers
101 views

Implicit differentiation dx/dt? [closed]

I am trying to find $\frac{\partial t}{ \partial y}$ as a function of $x$, $y$ and $\frac{\partial t}{\partial x}$ if both $x$ and $y$ depend on $t$ for the function ...
1
vote
0answers
96 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 ...
1
vote
2answers
74 views

Problems in animating graphs and its extrema

I tested to animate 2D graph and its extrema for simple case using Mathematica. ...
1
vote
0answers
30 views

Hidden assumption in Mathematica integration [duplicate]

If I do Integrate[Exp[I*omega*t],t], it gives me $\frac{1}{\omega} e^{i \omega t}$, as expected in most of the cases, except when $\omega$ is 0. Mathematica seems ...
0
votes
1answer
59 views

Plotting a function based on complicated integral

I have this function : f[Lambda_] := K Integrate[x Exp[- x^2-Lambda x] HypergeometricU[-Lambda,1/2,(x+ Lambda/2+2)^2],{x,0,Infinity}]; where ...
3
votes
1answer
88 views

Euler-Maclaurin summation

I want to compute asymptotic approximations to partial sum of harmonic series in Mathematica, using Euler-Maclaurin summation formula. ...
1
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1answer
69 views

Product derivative on derivative [closed]

this is a silly question, probably. How to product derivative on derivative in Mathematica. I mean for example how to achieve this result: Just more explanation. I need this for solving task with ...
1
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1answer
74 views

How to calculate the derivative at a point of a non-integrable multivariable function?

I want to integrate this function with respect to θ1 and then take the derivative of that function with respect to n. Since the ...
2
votes
1answer
78 views

How to plot linear term of a function expanded by Taylor seires in Mathematica?

I am quite new in Mathematica and I am trying to plot a linear term of a particular function in Mathematica. I have tried something like this: ...