Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

learn more… | top users | synonyms (3)

11
votes
1answer
126 views

How can I obtain an asymptotic integral expansion at infinity?

I want to find the asymptotic expansion at $x \to \infty$ of the following function: $$ I(x) \equiv \int_0^{\pi/2} e^{-xt^3 \cos(t)} dt.$$ To do this I defined the function ...
2
votes
1answer
54 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
31 views

How to find limit of this? [on hold]

$\displaystyle\lim_{x\to 0}^{}\sin{x}^{x}$ i tried this $ P =\displaystyle \lim_{x\to 0}(\sin{x})^x$ taking Natural log on both side we get , $log_{e}P= \displaystyle \lim_{x\to ...
3
votes
6answers
804 views

Compute Triple Integral on spherical coords

I need to compute: $\int \int \int z dxdydz$ over the domain: $\{x^2+y^2+z^2\leqslant 16,z\geqslant 0\}$ Im trying to use spherical coords as: $$\int_{0}^{2\pi} \int_{0}^{\frac{\pi}{2}} ...
4
votes
4answers
1k views

Numerical differentiation methods

Is it possible to write code in Mathematica that implements various differentiation methods (like forward, central, extrapolated, etc.)?
1
vote
1answer
286 views

Error Function Integral (Erf)

Any idea how to solve analytically this integral Integrate[(a Erf[a Sqrt[b/(a^2 + b)] c])/(a^2 + b)^(3/2), a] I tried substitution u=a^2 + b, but it didn't work. ...
0
votes
1answer
89 views

Limit of a sum as number of terms approaches ∞

Is it possible to find the limiting value of function at large N? ...
-3
votes
0answers
51 views

why this integral is out of compute? [on hold]

it doesn't work when I enter such integral, why and how to solve it?
2
votes
1answer
63 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 ...
8
votes
2answers
302 views

About an infinite product

I have a curiosity as regards the infinite product below. I wonder why Mathematica v.8.0. says the limit is $1$. This is not true. ...
3
votes
2answers
125 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: ...
1
vote
3answers
129 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}]
0
votes
1answer
187 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 ...
5
votes
2answers
127 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 ...
4
votes
0answers
69 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
32 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 ...
-3
votes
0answers
32 views

Find an example of continuous but not increasing function whose inverse function doesn't satisfy the Inverse Theorem [closed]

I have to find an example of a function $f : [a, b] → R$ which is continuous, but not strictly increasing, such that no inverse function $f^{ −1}$ satisfy the property of the Inverse Theorem.
1
vote
0answers
39 views

Calculating perturbative expansion in qft

Is there an easy way to use mathematica to take functional derivatives to do perturbation theory in qft? I know there is a package for functional derivatives, but can I get an example of how to use it ...
-2
votes
0answers
40 views

Multiple limits in Mathematica [closed]

In Maple there is a "replacement" operation where you basically replace a variable by anything you like, it's like taking a limit basically. How can one take a similar limit in Mathematica e.g. ...
0
votes
0answers
36 views

About the derivation of vector [closed]

We know that the derivation of the function in the attached picture is aij. But how to use Mathematica to calculate this? I am new in Mathematica, thanks so much for your response!
5
votes
2answers
385 views

Probability: Calculating a multiple integral

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=2,5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Cauchy Distribution having location parameter $\mu_{10\times 1} = ...
0
votes
0answers
16 views

Infinite series [migrated]

Good afternoon. I'm brazilian, then sorry by my bad english. I have a problem with one question about Infinite Series. I searched for anyone method could help me. I have all constants values (w, y, ...
5
votes
0answers
100 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 ...
9
votes
1answer
297 views

solve ODE with divergencies

The solutions of the second order differential equation $$\frac{1}{\eta}\frac{d}{d\eta}\left(\eta \frac{df}{d\eta}\right)+\left(1-\frac{s^2}{\eta^2}\right)f-f^3=0$$ is shown in Fig. 5.2 below, for ...
2
votes
0answers
30 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
25 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 ...
1
vote
1answer
37 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
30 views
4
votes
3answers
152 views

About the wrong evaluation of an integral

Here is an integral I've been studying in my research and I've just realized that Mathematica $8.0$ is unable to correctly compute it. I have 2 simple questions to ask: Is my code below correct? ...
2
votes
1answer
77 views

Double integral over normal pdf gives inconsistent answer

I am using Integrate function to do the following double integral ...
2
votes
1answer
73 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 ]: ...
10
votes
4answers
355 views

Correct way to integrate a certain function

I want to integrate $$ \int_{0}^{2\pi} dt_1 \frac{a + b*\cos(t_1 - t_2)}{c + d*\cos(t_1 - t_2)} $$ where $a, b, c, d, t_2$ are real numbers and $c + d > 0$ & $0 \leq t_2 \leq 2\pi$. I used ...
7
votes
6answers
999 views

Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$

Consider the function f[x_] := x Sin[Pi/x] I want to prove that this function is increasing for $x\ge 1$. This can be done with the first derivative. We have to ...
26
votes
1answer
352 views

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

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 now all returns unevaluated! I am hoping ...
2
votes
0answers
58 views

Strange Integrate messages / $RecursionLimit being ignored

Introduced in 10.1.0 The following behavior was observed in Mathematica 10.1 (Windows 64 bit) When attempting to evaluate the following integral, Mathematica outputs several messages which appear ...
4
votes
1answer
131 views
0
votes
1answer
65 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 ...
10
votes
4answers
3k views

How can I differentiate Numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
5
votes
1answer
146 views

Integration over a convex combination of a region: $\int_{\Omega} (w_1 z_1 + w_2 z_2)^{1-\sigma} d (z_1, z_2)$ where $\Omega = \{ z_1 + z_2 = 1\}$

Take $w,z\in R^{n}$. I am interested in integrating (as generically if possible) $$\int_{\Omega}(w \cdot z)^{1-\sigma} d z$$ Where the domain of $\Omega$ is $1$ dimension, and includes the convex ...
4
votes
1answer
1k views

Lie-Bracket of two vector fields

I'm new to Mathematica (installed couple of hours ago) and I need to compute a few Lie brackets between two vector fields $f$ and $g$. $$ f\left(\mathbf{x}\right) = \left( \begin{array}{c} ...
0
votes
1answer
49 views

Adapt the code to produce a three column table containing the values of n, etc. (Numerical integration)

Here is a “procedural” program that we wrote in my class, implementing the rectangle rule of numerical integration: ...
0
votes
0answers
43 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 ...
0
votes
0answers
34 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 $s$: ...
-1
votes
0answers
26 views

Adapt the code to produce a three column table (rectangle rule of numerical integration) [duplicate]

I was given the following program implementing the rectangle rule of numerical integration: ...
7
votes
0answers
48 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
139 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
73 views

Four integrals, how can I expedite the calculations?

I have to calculate the following multiple integrals (4 integrals) ...