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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5
votes
1answer
94 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 ...
2
votes
1answer
110 views

Computing a Gamma function-Gaussian integral

I would like to compute the following function: Integrate[Gamma[k,0,Exp[-2 e x^2]],x] k is an integer and ...
2
votes
3answers
231 views

How do I find the area between two polar curves?

More specifically above r=6 and below r=4+4cos(θ) graph of the two curves PolarPlot[{6, 4 + 4 Cos[t]}, {t, 0, 2 Pi}]
5
votes
2answers
228 views

Double improper integral

I am trying to compute the following double integral: Integrate[(r BesselJ[0, r])/( 2 (r^2 + z^2)^(1/2)), {z, -Infinity, Infinity}, {r, 0, Infinity}] Which ...
5
votes
0answers
162 views

Integral formula for the inverse Laplace transform doesn't work?

The direct implementation of the definition of the inverse Laplace transform using Integrate fails in the following case: ...
1
vote
0answers
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 ...
0
votes
0answers
75 views

Multiple Integral of equation including dx prime?

I'm hoping someone can verify I've written this function properly since I'm a little new to Mathematica. What I'm attempting to do is code a function that describes a gravitational field of an ...
7
votes
2answers
331 views

Integrate fails for generic parameters but works for any specific values (v. 10.0.x bug)

Bug introduced in 9.0 and fixed in 10.1 I was trying to get the following integral ...
0
votes
1answer
119 views

Limit of a sum as number of terms approaches ∞

Is it possible to find the limiting value of function at large N? ...
7
votes
2answers
455 views

Integrating a function over a surface integral

From a first principles bandstructure calculation I get an energy scalar field in three dimensions $E(x,y,z)$. It's now easy to plot a constant energy (contour)-surface for dedicated values ...
3
votes
2answers
152 views

Strange results from evaluating a simple integral

I am trying to do a seemingly simple integral in Mathematica 10 and am getting strange results: ...
10
votes
1answer
258 views

Contour Integration along a contour containing two branch points

I need to compute following contour integrations: $$f(u)=\oint_\alpha dz \sqrt{z^3+z+u} \qquad ; \qquad g(u)=\oint_\beta dz \sqrt{z^3+z+u}$$ In which $\alpha$ and $\beta$ are two contours in ...
4
votes
2answers
125 views

Imaginary terms in the derivative of Jacobi theta function (2) on the real line

I am trying to calculate/plot the derivative of the second Jacobi theta function $d\theta_2(0, e^{-\pi t} )/dt$. Calculating or plotting the function itself works fine: ...
2
votes
0answers
78 views

How do I numerically integrate over a data set that has uncertainties? [closed]

I have a 1D data set {xi, yi} with no uncertainties in xi and with uncertainties dyi in yi. The resulting discrete function is monotonic and relatively smooth and I would like to integrate the ...
0
votes
2answers
56 views

Integrating expressions with several terms and delta functions

So I want to integrate an expression that looks something like this: Integrate[f[x]+DiracDelta[x-y]g[x],{x,-Infinity,Infinity}] With some more terms added with ...
2
votes
1answer
91 views

Forcing Exact Outputs for Integrate [closed]

I'm trying to compute the following triple integral: ...
1
vote
1answer
92 views

Partial derivative of defined function with vector input

Background: Have written a formula for the refractive index for a glass slab (n) that depends on the variables t,a and d. Now I want to calculate for example some sort of error and I'll be needing to ...
0
votes
1answer
56 views

Boundary condition not correctly imposed for NDSolve

I notice that when plotting the below NDSolveValue ...
2
votes
1answer
88 views

an Integral that should be doable:

Integrate[Cos[\[Beta]] Exp[I z Cos[\[Beta] - \[Alpha]]], {\[Beta], 0, 2 \[Pi]},Assumptions -> z \[Element] Reals] correct answer is [ I think ]: ...
9
votes
1answer
255 views

Why don't products of Dirac deltas integrate correctly?

Bug introduced in 10.0.0 and fixed in 10.0.1 The integral $\int \int \ \delta(x) \delta(y) \ dx dy=1$ evaluates to 0 in Mathematica ...
3
votes
1answer
106 views

Strange Integrate messages / $RecursionLimit being ignored

Bug introduced in 10.1.0 and fixed in 10.2.0 The following behavior was observed in Mathematica 10.1 (Windows 64 bit) When attempting to evaluate the following integral, Mathematica outputs ...
0
votes
2answers
93 views

Fix my code to return a table of values

Here is a “procedural” program that we wrote in my class, implementing the rectangle rule of numerical integration: ...
-1
votes
1answer
55 views

It is possible to calculate a two vector integral

I have this problem: calculate the integral of: -1+Sqrt[2*d+1] with d being a distance of two points in a 60$\times$60 box ...
28
votes
1answer
437 views

many indefinite integrals do not evaluate in 10.1, looking for the cause

Bug introduced in 10.1 and fixed in 10.2 Many integrals no longer evaluate in V 10.1 when they did in 10.0.2 Here are some 23 integrals as an example, that all produced results in V 10.0.2, but ...
0
votes
0answers
45 views

Calculus with Mathematica, books, interesting examples [duplicate]

I'm looking for a book where I could find informations and interesting examples regarding examine functions of one variable like continuity of functions, limits, differentiability in Mathematica. I'd ...
4
votes
1answer
142 views

Mathematica does not help in this integral

I am trying to solve this integral with assumptions: ...
1
vote
0answers
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 $s$: ...
0
votes
1answer
70 views

Can't obtain a closed form expression for an integral

I am trying to find the result of quite a complicated double integral. While the first part (being a Principal value integral) gave no particular problems, the second one is not providing any closed ...
8
votes
0answers
68 views

Finding simplifying substitutions for an integral involving limits and integrand

[The following is based on a William Lowell Putnam Mathematical Competition problem.] Consider the definite integral: $I = \int\limits_2^4 \frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\sqrt{\log ...
2
votes
3answers
173 views

How can I get the exact value minimum of this function?

I want to find min of the function $$\frac{1}{\sqrt{2 x^2+\left(3+\sqrt{3}\right) x+3}}+\frac{1}{\sqrt{2 x^2+\left(3-\sqrt{3}\right) x+3}}+\sqrt{\frac{1}{3} \left(2 x^2+2 ...
0
votes
1answer
82 views

Four integrals, how can I expedite the calculations?

I have to calculate the following multiple integrals (4 integrals) ...
5
votes
2answers
386 views

How can I get the inverse of my function?

The original function is $$f=\frac{1}{e^{\frac{\phi }{k t}}-1}-\frac{m+1}{e^{\frac{(m+1) \phi }{k t}}-1}$$ I want to express $e^{\frac{\phi }{k t}}$ about $m$ and $f$, so I tried: ...
0
votes
1answer
171 views

PDE of real-world system, integral boundary condition

I've stripped all the physical-significance for clarity, but I know that u[x,t] will be everywhere positive and continuous. here are the equations in Mathematica code: ...
0
votes
0answers
107 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)}) ...
1
vote
1answer
122 views

How can I simplify a triple integral with exponentials?

I want to simplify the following triple integral with exponential terms. \begin{equation} \int_0^\infty\int_0^\infty \int_0^\infty \frac{1}{R\,G} e^{-p(1+R\,a)-q\, b \frac{1+R\, a}{1+G\, x}}\, ...
6
votes
1answer
407 views

Lagrange Multiplier

We are asked to maximize and minimize $f(x,y)=4xy$, given the constraint $4x^2+y^2=8$, using the Lagrange Multiplier method. First, I enter the functions f and g. ...
4
votes
2answers
137 views

Well-defined symbolic integral leading to ConditionalExpression

I would like to determine a closed-form expression for the following symbolic integral $$ \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} x \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} y \, \frac{1 + b x + c y}{1 + e ...
3
votes
3answers
70 views

Multiple integrals where the number of integrals is aribtrary

I know that I can do, say, a triple integral such as $$\int_{a_x}^{b_x}\int_{a_y}^{b_y}\int_{a_z}^{b_z}f(x,y,z)\,dz\,dy\,dx$$ with the input ...
-5
votes
1answer
75 views

Show steps to compute limit [closed]

I'm trying to use Mathematica to compute a limit, because I have no idea how to compute it by myself. The limit should be: $$\lim _{n\rightarrow \infty }\dfrac {2^{n+1}-n-2}{2^{n}}$$ Any ideas?
0
votes
2answers
203 views

Multidimensional Numeric Integration

I can't manage to calculate numerically the following multidimensional integral: ...
0
votes
1answer
161 views

Cauchy Principal Value integral- no result is obtained [closed]

I have a particular Cauchy Principal Value integral that I need to numerically solve for my thesis research. It is the following $$ ...
4
votes
2answers
265 views

Using Mathematica to confirm Bernoulli's inequality

I have several challenges that I want to confirm is true. I have chosen this one because it is rather simple (proof by induction). There are times when I do not want to spend ages trying find proofs. ...
0
votes
0answers
27 views

Use implicit differentiation to find the slope of the tangent line to the curve 4 xy^3+ 5 xy= 45 at the point ( 5 , 1 ) [duplicate]

Use implicit differentiation to find the slope of the tangent line to the curve 4 xy^3+ 5 xy= 45 at the point ( 5 , 1 )
1
vote
2answers
137 views

Is there a way to do a cyclic convolution analytically in Mathematica?

Let's say I want to convolve a Gaussian function Pulse[t_] = Exp[-(t - Mid)^2/(2 sig^2)]; with an exponential broadening function ...
6
votes
2answers
424 views

Convolve does not get the correct answer

Convolve[Sinc[x], Exp[-x^2], x, X] (* E^-X^2 π *) is obviously false, but why? Any suggestions ?
3
votes
3answers
116 views

How to Integrate trivial products of DiracDelta

A long while ago I was able to integrate with Mathematica: $$\int_0^1 \delta(1-x)\delta(x) f(x) \,dx = 0$$ using ...
0
votes
1answer
121 views

How to do this triple integral?

I have a triple integral which is kind of complex, and I want to use Mathematics to help me do the integral. However, when I press "Enter" and "Shift" the software get stuck. I wonder whether this ...
0
votes
2answers
177 views

Finding the equation of tangent lines where a function has a specified slope [closed]

A function is defined as f[x_] := 3x^4 + 8x^3 - 24x^2 - 48x + 19 I need to find the equation of the tangent lines at the points where the tangent line has a ...
2
votes
5answers
302 views

Simplify an integral involving trigonometric functions

We were doing variation of parameters in differential equations tonight and had to do the following integral, the result given by hand calculations. $$\int \cos t\tan^2 t\,dt=\ln|\sec t+\tan t|-\sin ...
1
vote
1answer
75 views

Integrating with assumptions and limits of integration [duplicate]

I have an integration with assumptions and limits of integration. I tried to use Mathematica to solve this problem, but I cannot get any results. ...