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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0
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0answers
60 views

Why can't Mathematica simplify this expression involving conjugate of complex expression?

In theory it should recognise that all terms are real, and drop the Conjugate attribute. Any clues why this might be so?
2
votes
2answers
143 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
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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
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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 [on hold]

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
713 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
197 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
84 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
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1answer
104 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
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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
161 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
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1answer
167 views

Understanding output of multivariable integration

I'm new to Mathematica and I'm trying to integrate this function: ...
0
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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
247 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
821 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
793 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
81 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
228 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
612 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?