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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3
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0answers
61 views

Using NIntegrate and DiscretePlot to visualize pseudodifferential operators

In harmonic analysis, pseudodifferential operators are a way to generalize the notions of derivatives, through the use of Fourier transforms. The basic idea being, Let ...
2
votes
2answers
146 views

How to solve this two algebraic equation simultaneously for u and H ?(all real number)

I want to find the non-zero value of H when beta is changing(especially what value of beta when increasing will there be a non-zero H value). H is between [0,100]. This is actually the calculation ...
-3
votes
0answers
34 views

integral-equation of Wentzel–Kramers–Brillouin [on hold]

I need a code that can help me to solve the WKB equation for the eigenenergies for any given potential
1
vote
3answers
112 views

Differentiation help [on hold]

I am new in Mathematica. I want to differentiate ...
0
votes
0answers
66 views

NIntegrate unexpectedly returns complex number [closed]

I am attempting to visualise the effect of shifting parameter $\gamma$ on the 3-parameter log-normal distribution. $$pdf(x;\mu,\sigma,\gamma) = ...
0
votes
1answer
247 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
16
votes
1answer
154 views

How to determine if a function is continuous?

I wish to write code for Riemann Stieltjes integrals in Mathematica. A necessary condition for the theorem to hold is that the function must be continuous. The domain of the function is a closed ...
5
votes
1answer
156 views

Fitting a Parametric Curve

I apologize if this question is obvious or simple. I'm in high school and have started playing around with Mathematica only recently. For my Calculus Final, I am supposed to use rotation about the ...
17
votes
1answer
714 views

Dual complex integral over implicit path using contour plot

Context I am interested in doing double contour integral over paths which are defined implicitly. For the sake of debugging, let's assume its $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
3
votes
1answer
198 views

Derivatives of functions with arbitrary number of variables?

I am trying to define a function f[x1,x2,...,xn] with n integer but not specified. And then I would like this funktion to behave ...
1
vote
1answer
85 views

Computing a binomial series

How can I compute the following series: Module[{n = 10^6}, Sqrt[n] * (4^-n) * NSum[Binomial[2*n - 1, n - k]/((2 k - 1)^2 + Pi^2), {k, 1, n}]] including ...
3
votes
1answer
37 views
1
vote
1answer
65 views

How to change variables in expressions with derivatives

I have the following function: K[r_, h_] = -(D[h[r], {r, 2}] + D[h[r], r]/r + D[h[r], r]^3/r)/(2 (1 + D[h[r], r]^2)^(3/2)) In order to non-dimensionalize it, I ...
0
votes
1answer
105 views

Integrate does not work on my expression

I am trying to integrate a simple equation. The code is as follows ...
0
votes
1answer
68 views

Integrate works but NIntegrate doesn't

I have a complicated integral function that I'm trying to evaluate, which will have to be done numerically. I wanted to try a simpler one first, one that has an analytic form, because I could check ...
9
votes
5answers
4k views

Notation of partial derivative

I want to write partial derivatives of functions with many arguments. Why is it that when I type f[x,y] ctrl+6 (0,1) it turns out to be bad syntax? The output of ...
0
votes
1answer
86 views

Strange behavior of `FourierSinCoefficient`

FourierSinCoefficient works normally like this and the result is checked with Integrate. ...
0
votes
1answer
82 views

Singular integral mathematica

A = Integrate[Sin[2 x] / (A1 - B1 Sin[2 x] + C1 Cos[x] - D1 Sin[x]), {x, 0, 2 Pi}] The calculation is taking too much time; not returning any results. Any help?
-1
votes
3answers
249 views

Defining an alternative derivative function?

I want to calculate the derivative at a point, but I do not want to use the built-in derivative function D. I began with this definition of the derivative , ...
3
votes
3answers
163 views

Plotting the region bounded by parallel lines

I am working on the integral $$\int\int_D (2x+y)^2 e^{x-y}dA,$$ where $D$ is the region bounded by $2x+y=1$, $2x+y=4$, $x-y=-1$, and $x-y=1$. I need to shade the region bounded by these lines, so I ...
4
votes
2answers
109 views

Symmetrise a complicated expression

I am calculating the derivatives of a symmetric function $F(a_1, a_2)$ and got very complicated expressions, which I'd like to write in a symmetric form with respect to $1 \leftrightarrow 2$ (clearly ...
2
votes
1answer
91 views

How to simplify and evaluate Integral with lots of DiracDelta dists

I have a question about an Integrals which I can do by hand but I want to implement this Integral in Mathematica. Actually it is the definition of a 2 Particle Phase Space. The Expression is the ...
2
votes
1answer
156 views

Integral of GeneratingFunction

I know that GeneratingFunction can be used to compute the generating function $\sum_{n=0}^\infty a_n x^n$ of a sequence $(a_n)_n$ via GeneratingFunction[a[n],n,x] ...
1
vote
2answers
209 views

Symbolic integral with distributions

Why is Integrate[ HeavisideTheta[1 - x^2] DiracDelta[1 - x^2] , {x, 0, 1} ] (*0*) It should be HeavisideTheta[0]?
0
votes
1answer
167 views

Understanding output of multivariable integration

I'm new to Mathematica and I'm trying to integrate this function: ...
0
votes
0answers
132 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. The equation below presents the final form ...
9
votes
1answer
155 views

When to use GenerateConditions -> True

Many functions, usuallly those involving integration, take a GenerateConditions option which often defaults to False, or at ...
11
votes
1answer
217 views

What exactly does GenerateConditions do?

Consider for example this strange behavior: Integrate[1/x, {x, 0, Infinity}, GenerateConditions -> False] (*0*) I'd also like to know the difference between ...
3
votes
1answer
109 views

Strange integration

Bug introduced in 9.0 or earlier and fixed in 10.1 Note: Beginning with V10.1, this integral returns unevaluated but without error messages. I tried to evaluate this line ...
2
votes
1answer
248 views

How to evaluate this integral?

Why can it not evaluate this integral? Please help. Integrate[Exp[-r^2]* r^2*Log[Exp[-r^2]* r^2*(2.5 - r^2)*(2.5 - r^2)], {r, 0, 10}]
9
votes
1answer
184 views

Wrong Limit with LaguerreL

Bug introduced in 7.0 and fixed in 10.2.0 Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞] Mathematica (wrong) output ...
5
votes
1answer
148 views

Visualize transformation used in multiple integration

In class, we will sketch the region $D$ in $R^2$ bounded by the curves $xy=1$, $xy=4$, $y=x$, and $y=x+2$. Then we will use the change of variables given by $u=xy$ and $v=y-x$. We need to show that ...
4
votes
3answers
278 views

How to do algebra on unevaluated integrals?

I am working with functions calculated from a set of general basis functions. ...
10
votes
2answers
823 views

Is Mathematica really getting this limit wrong?

Bug introduced in 5.1 and fixed in 10.0.2 I'm trying to calculate: $$ \lim_{\beta \to \infty} \tanh \left( \beta A \right) = \mathrm{sgn} \left( A \right) $$ for $A \in \mathbb{R}$, $\mathrm{sgn} ...
20
votes
1answer
541 views

Incorrect result from Integrate

Bug introduced in 8.0 and fixed in 10.0 I attempted to calculate the following integral: ...
7
votes
1answer
129 views

Old fashioned region method?

Just stumbled across this idea in http://users.rowan.edu/~hassen/Mathematica/Volume%20III/Chapter%2015.pdf. ...
12
votes
1answer
794 views

1/x integration giving 0 instead of infinity [duplicate]

I stumbled across the fact this integral: Integrate[1/y, {y, 0, 1}, GenerateConditions -> False] returns 0 Anybody ...
0
votes
0answers
57 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] ...
5
votes
1answer
82 views

Second derivative of SmoothKernelDistribution PDF?

Does anyone know why I can't seem to get a second derivative of this interpolating function f? In this example, h[x] is zero ...
3
votes
1answer
2k views

Laurent series expansion

Can someone share how to find a Laurent series expansion of $$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$ centered at zero on the annular disk $1<|z|<2$?
1
vote
3answers
229 views

finding an argument of a complex number

What is the simplest way to find the argument of the following function? ((1 - E^((I π (1 - α))/(β - α)) z)/(1 - E^(-((I π (1 - α))/(β - α))) z)) as I tried the ...
8
votes
1answer
613 views

Numerical contour integrations in the complex plane - contour deformation gives different answer for analytic kernel

I am trying to do a contour integration in Mathematica numerically. In particular, I'm checking the identity: $$ H_m^{(1)}(z) =\frac{i^{-m}}{\pi}\int_{-\pi/2 + i \infty}^{\pi/2 - i \infty} \exp[i m ...
4
votes
1answer
497 views

Multi-dimensional integral in the complex plane with poles and essential singularity

I've passed the last week searching a way to numerically integrate this multi-dimensional integral in the complex plane at the poles and avoiding the singularity at z=0: $$ \oint_{C}\oint_{C\ auound\ ...
2
votes
1answer
44 views

Derivative of conjugate multivariate function

I have a problem with Mathematica, taking the derivative of the conjugate of some function. I know that a similar question has been posed before here, but the solution did not work for multivariate ...
0
votes
0answers
5 views

Problem with Integration using substitution [migrated]

OK, so here is a question from integration that I recently stumbled upon. Evaluate $I =\int\cos^3\theta\sin\theta\,d\theta$ Now here's how I tried to solve it first; $Substitute \cos\theta = t$ ...
4
votes
4answers
406 views

$L = \lim\limits_{z \to 1} \frac{1-z}{1-z^\ast}$ evaluates incorrectly

I'm about 90% certain this is a Mathematica issue, not me making a silly mistake. I'm trying to evaluate $$L = \lim_{z \to 1} \frac{1-z}{1-z^\ast}.$$ Naively entering ...
0
votes
1answer
2k views

Complex line integral

Can someone recommend an online article or introductory tutorial that will show me how to do real and complex line integrals using Mathematica?