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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4
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2answers
356 views

Real integral giving imaginary answer

Hello I am trying to evaluate the following integral Integrate[4279/Sqrt[0.6817 + 0.3183*(1 + x)^3], {x, 0, 20}] my mathematica 9 gives me ...
4
votes
1answer
313 views

Integrate over piecewise function defined using /;

f[x_] := x /; x<0 f[x_] := x^2 /; x>=0 Integrate[f[x],{x,-1,1}] The above does not work (Mathematica returns it unevaluated), but the below does. ...
4
votes
1answer
232 views

Problem on limit involving complex numbers

I have $${\frac{(6 k+1)^{k}}{(2 k+5)^{k}}}*(z-2 i)^k$$ and I need to find it's limit for $k$ approaching infinity. ...
4
votes
1answer
226 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
4
votes
2answers
240 views

Function given exact arguments returns hugely different value than it returns when given equivalent inexact arguments

I was trying to compute the probability that a coin is from a particular underlying distribution given that a particular set of tosses was observed. (I know this can be done in a different way, but I ...
4
votes
1answer
156 views

Volume within parameter space

Imagine a parameter space with variable 0<p<1, 0<e1<1/2 and 0<e2<1/2. ...
4
votes
1answer
219 views

The limit of a product to infinity

What is the difficulty with this question to Mathematica? Is it just a problem with Mathematica v.8.0 or all versions are in trouble with it? Or is something wrong with my input? ...
4
votes
1answer
2k views

finding poles of a function

Is there a command to find the poles of a function $f=f(z)$? example: let $$f(z) = \frac{1}{z^2-1}$$ then we know that the poles are at $z=\pm 1$ but is there a special command in mathematica to do ...
4
votes
1answer
542 views

Order of integration changes output of indefinite multiple integral in Mathematica 7

I'm trying to integrate a form-factor used in the calculation of radiation between two rectangles in perpendicular planes. While the integral is usually done over fixed limits, I am trying to do the ...
4
votes
2answers
213 views

How to force correct answers for Integrals of Cos[mx]*Cos[nx]? [duplicate]

This is a big problem if you do anything with a Fourier Series. This statement: Assuming[Element[{m, n}, Integers], Integrate[Cos[m*x]*Cos[n*x], {x, 0, 2 Pi}]] ...
4
votes
3answers
290 views

Creating a function with integral zeroes of the 0th, 1st, and 2nd derivatives

I would like to be able to randomly generate functions, each of which satisfies $f : [-10, 10] \rightarrow [-10, 10]$ All the zeroes, critical points, and inflection points have an integral ...
4
votes
2answers
288 views

How do I evaluate a symbolic integral involving Hermite polynomials?

I want to test a difficult integral : Integral on all reals of some complicated function involving the Hermitian polynomials, exponentials, squares, factorials, and being general considering any ...
4
votes
4answers
332 views

Differentiating space curves

I'm trying to do some very basic differential geometry of space curves. For example, a space curve $\gamma:\mathbb R\to\mathbb R^3$ has unit tangent and normal vectors given by ...
4
votes
1answer
778 views

Computation of parametric integral

I am trying to compute the integral Integrate[(g^(u^(g - 1)))/(1 + u^g), {u, 0, t}] but as an answer I get my input expression. There must be something wrong ...
4
votes
1answer
152 views

Efficient Dyson series implementation

I'm trying to implement a Dyson series \begin{array}{lcl} U(x,x_0) & = & 1 + \int_{x_0}^{x}{dy_1V(y_1)}+\int_{x_0}^x{dy_1\int_{x_0}^{y_1}{dy_2V(y_1)V(y_2)}}+\cdots \\ & &{} + ...
4
votes
2answers
121 views

Inconsistent results for equivalent converging symbolic integrals

I have looked at previous questions and I'm aware that this seems to be a known bug: Mathematica giving inconsistent results for symbolic integrals done in different ways. The origins for the bugs ...
4
votes
2answers
117 views

Limit won't compute

Does anyone know why the limit: ...
4
votes
1answer
189 views

Why does Assuming for Integrate not work as expected?

I'm trying to perform the following integral with Mathematica 7: ...
4
votes
1answer
160 views

How to plot the result of this singular integral?

Please I open a new post here after this one : http://mathematica.stackexchange.com/a/59203/10158 Now I want to plot the function $f(a,b)$ as a function of $b$ for different values of $a$ : $a=0.5$ , ...
4
votes
2answers
194 views

Integrating a periodic function

I have a periodic function ff: ff := Function[x, Piecewise[{{ff[x - 1], x >= 1}, {2 x, 0 <= x < 1}, {ff[x + 1], x < 0}}]] Plotting it works fine: ...
4
votes
2answers
388 views

Using units and piecewise functions in Integrate

For simple cases, Quantities appear to be handled well by Integrate: ...
4
votes
2answers
138 views

Strange behavior of Integrate

I'm trying to calculate the following integral using Mathematica 9.0.1.0 a11=Integrate[Abs[Sin[b+x]],{x,0,2*\[Pi]}] This should be a simple problem; however, it ...
4
votes
1answer
439 views

Integrating over Bessel Function erroreous? (Hankel Transform)

Bug introduced in 8.0.4 or earlier and persists through 10.0.2. The Hankel Transform is given by Integrate[f[x] x BesselJ[0,x t],{x,0,Infinity}] It is ...
4
votes
1answer
1k views

Is it possible to impose “Assumptions” in DSolve or equivalent? (differential equation solving)

When DSolve tries to solve differential equations, it is sometimes not smart enough to generate conditions according to different possible value of parameters. ...
4
votes
0answers
199 views

Strange result from evaluating a Limit expression

When I evaluate the limit of (1-Cos[x]) Sin[1/x] at x = 0 in Mathematica 9, I obtained ...
4
votes
0answers
149 views

Version 8.0 integrates but Version 9.0.1 doesn't

I am trying to run the following integral in version 9.0, but it fails: ...
3
votes
3answers
444 views

Symbolic derivative of $n$-term product

I want to determine the relationship that must exist between the $x_i$ and $y_i$ such that $$ \frac{\partial}{\partial\theta} \prod_{i=1}^n \frac{f(x_i,\theta)}{f(y_i,\theta)} = 0, $$ where $$ ...
3
votes
2answers
279 views

Integral converging in M9 but not in M10

Background: Mac OSX 10.9.4, Mathematica 9.0.1 vs. Mathematica 10.0 (both versions are Student Editions). I have a notebook. It used to evaluate fine in Mathematica 9. I upgraded to 10 and, without ...
3
votes
2answers
322 views

Incorrect value of infinite sum

Wolfram Alpha and Mathematica give an incorrect result (numerically) for the following infinite sum: ...
3
votes
2answers
414 views

Write a function that returns the logarithmic derivative

How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
3
votes
2answers
3k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
3
votes
5answers
216 views

A double series with divisibility restrictions

How may I restrict $i,j$ such that they run over $\mathbb{N}$ excepting the numbers divisible by $2$ or $3$ or $7$? ...
3
votes
2answers
389 views

Create polygon using edge lengths and area

Four-sided convex land plots are usually denoted with edge lengths and area. How do I create a Polygon Object with these parameters in Mathematica ?
3
votes
3answers
158 views

Factoring a scalar function out of a vector

I've taken a first and second derivative: ...
3
votes
2answers
249 views

Computing the minimum distance in a contour plot

I have the following Mathematica code ...
3
votes
2answers
201 views

How to find the maximum of this function on the positive real line?

I need to maximize this function on the positive real line: $$ \frac{1}{\Gamma(x)^{14}}\cdot\frac{1}{{\frac{323.6}{14x}}^{14x}}\cdot(1.22578*10^{19})^{x-1}e^{-14x} $$ the correct answer should be ...
3
votes
2answers
156 views

Complex limit gives wrong answer

I'm evaluating $$\lim_{z\to e^{i \pi/2 n}} \frac{z-e^{i \pi/2 n}}{z^{2 n}+1}$$ with Mathematica 9.0.1: ...
3
votes
3answers
198 views

What is the formula for this numerical series?

I'm developing a questions game. My goal is that the score for each correct answer will increase as the user answers more questions. Initially there are 15 points for each correct answer. Every 4 ...
3
votes
3answers
300 views

Proving a recurrence in Mathematica

I have $$j_n=\int_0^1 x^{2n} \sin(\pi x)dx.$$ How do I show that $$j_{n+1}= \frac{1}{\pi^2}(\pi- (2n+1)(2n+2)j_n)\, ?$$ I keep getting a recurring integration by parts and I can't simplify it. ...
3
votes
2answers
106 views

Integration of a Rational Function returns RootSum[]

I am trying to solve an integral given below: Integrate[r^2/(-α r^3 + r^2 - 2 m r + Q^2), r] but since coefficients of this cubic polynomial are as parameters, ...
3
votes
1answer
205 views

Convergence in NIntegrate vs Integrate

I am faced with this situation that for a certain integration, $\int _0 ^\infty \frac { \tanh (\pi \sqrt{x} )} {\sqrt{x+10} } dx$ - the command Integrate returns ...
3
votes
3answers
55 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 ...
3
votes
2answers
498 views

Color a Function by its Derivative

Mathematica's ColorFunction seems to struggle with coloring a function "y" by its derivative D[y,x]. This is a seemingly simple task, but Mathematica can't handle it. While I can certainly evaluate ...
3
votes
1answer
222 views

How to numerically integrate this integral

I am unable to do this definite integral in Mathematica 9. Is there any command so that I can get the numerical value of the above integration? Code: ...
3
votes
5answers
125 views

Using Mathematica to find a Derivative

I am given a system first order differential equations: $x'=y$ and $y'=6x^2-a/2$, where $a$ is a constant and $'$ denotes $t$-derivatives. I then make the substitution $(x,y)=(x_1y_1,y_1)$. This ...
3
votes
3answers
906 views

How to integrate a function over a 3D planar polygon?

I am trying to integrate a function over a planar polygon in 3D. In 2D, this is fairly straightforward, using either answer from this question (I use the second answer). If we use an equilateral ...
3
votes
1answer
143 views

Double Integral and Assumptions

I'm afraid this is going to be a really stupid question. Evaluating the following definite integral Integrate[Sqrt[1 - (x^2 + y^2)], {x, -1, 1}, {y, -1, 1}] ...
3
votes
1answer
149 views

Why is the output of my limit expression an interval?

Why is the output of the limit below an interval? It should be precisely $1$. ...
3
votes
1answer
136 views

Series approximation to integral

I would like to approximate the integral $$ \int_0^\infty dy\,\frac{1}{\sqrt{2\pi y\sigma^2}}\exp\left(-\frac{(x-y)^2}{2y\sigma^2}\right)f(y), $$ as a series expansion in the limit $\sigma\rightarrow ...
3
votes
2answers
375 views

How do I represent a system dynamics feedback loop?

In System Dynamics, if I want represent the relationship between Speed and Distances, I create a Flow (Speed) and a Stock (Distance) as you can see in this Insight Maker Sample . Heres an Image of how ...