6
votes
5answers
353 views

Find function inverse

I'm trying to find the inverse of a function: (30*x^2 (1 - x)^2) (* where 0<x<1 *) I tried all the following options: 1. ...
4
votes
0answers
152 views

Strange behaviour of MMA in derivatives of some standard functions

There are some peculiar things to be discovered in derivatives of some standard functions in MMA: Strange behaviour Example 1: Abs We have ...
5
votes
2answers
170 views

Is there a built-in function which detects singularities in a function?

Given a function f[x] and a region M in the complex x-plane, how can I find singularities of f in this region, i.e., issue a ...
8
votes
8answers
713 views

Finding maximum or minimum of implicit functions

is there any built in function that can be used to find maximum or minimum of implicit functions? For example, if we have the equation $$x^2 + y^2 = (2 x^2 + 2 y^2 - x)^2,$$ then we can visualize the ...
0
votes
1answer
60 views

Integrating function can't be epressed? [closed]

Hi I have a function in a form of $$\frac{a}{x}exp(\frac{b}{\sqrt{3}-x})$$ The code is Integrate[a/x*E^(b/(3^0.5 - x)), {x, 1, 3^0.5}] But it can't work ...
2
votes
2answers
87 views

Graphical solution of a a two-variable system containing an equation and an inequality

I'm currently studying atmospheric-gravity waves and their dispersion relations. I want to have look at values of $(x,y)$ that solve the following system : \begin{equation}\label{}(1) \left\{ ...
0
votes
1answer
42 views

Defining arbitrary order derivatives function [duplicate]

I have a function $\phi(t)$ and I want to define a function $\phi D(t,r):=\phi^{(r)}(t)$, in other words evaluate the $r$'th derivative of $\phi$ at $t$. The naive code that I have is: ...
6
votes
1answer
112 views

Is it possible to circumvent a bug inside SeriesCoefficient?

As far as I can tell, there seems to be a bug in SeriesCoefficient: ...
1
vote
0answers
139 views

Derivative of the Absolute Value Function in Mathematica looks very different from the actual answer

Derivative of the Abs Function in Mathematica looks very different than the actual answer. Why? How to correct this? For example I entered ...
0
votes
1answer
95 views

Evaluate integral of a series

I want to evaluate this integral, but it won't work. Does anyone knows why? ...
0
votes
1answer
43 views

Showing result of derivative and other functions [closed]

I have a problem with my Mathematica 7.0 When I write: Derivative[x^2, x] Mathematica returns as result : ...
1
vote
1answer
123 views

Function derivatives in arbitrary dimension

I have a higher dimensional function: $$f(x,t)=-\ln(t)-\ln(1-\left\|x\right\|^2-t^2)$$ where $x\in\mathbb{R}^n,~t\in\mathbb{R}$. I want to compute the derivatives with the commands ...
4
votes
1answer
140 views

Volume within parameter space

Imagine a parameter space with variable 0<p<1, 0<e1<1/2 and 0<e2<1/2. ...
5
votes
0answers
168 views

Strange Integrate behavior (a bug!)

The following two calculations should give the same result. After all, integration is a linear operation. I have pasted the code below in case you want to play with it. ...
3
votes
1answer
334 views

Integral of Lorentzian yields different results depending on when parameter assigments are made

I'm evaluating the integral of a Lorentzian, which I know equals one. First I define the function and evaluate the integral in two slightly different ways. Surprisingly, I do not get the right answer ...
3
votes
3answers
185 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 ...
14
votes
1answer
331 views

How to represent a continuous monotonic phase of Airy functions?

Note: In this question I am concerned only with real-valued variables and functions. DLMF, §9.8 Airy Functions, Modulus and Phase, formula $9.8.4$ defines the phase of Airy functions: ...
5
votes
2answers
659 views

How to find the non-differentiable point(s) of a given continuous function?

For example, the non-differentiable point of the function $f(x)=|x|$ is at $x=0$. How to find the non-differentiable points of a continuous function that is defined numerically?
1
vote
0answers
162 views

Positive integrand giving negative answer

I'm integrating a positive function f(t) times sin(t) from 0 to pi/5 and get -38. Actually f is slightly negative for a short time (smallest value ~ -0.0005), but far from enough to explain this. ...
6
votes
1answer
241 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
1answer
497 views

How to take the derivative w.r.t. an arbitrary function?

EDIT: The answer posted by @Jens works for built-in functions only. However I'm starting to wonder if this is related to my Mathematica install somehow. I have version 7. Here is an example in the ...
1
vote
1answer
159 views

Derivative inside a function

I am trying a problem that should be simple: to create a function that contains a derivative. I need to do a more complex example, but even with the simplest I'm having trouble: Let's consider ...
9
votes
1answer
332 views

Is it possible to find a limit of a sequence given by its recurrence relation?

I need to calculate a limit of a sequence given by its recurrence relation. I tried the following: ...
13
votes
1answer
254 views

How do I get a general form for n-th derivative of a function? [duplicate]

I tried the following but it basically returns unevaluated: ...
16
votes
4answers
5k views

Finding Limits in several variables

Is there a way to find a limit of a multivariable function, like $$\lim_{(x,y)\to (0,0)} f(x,y)$$ with Mathematica? When $f$ is continuous, we can use $$\lim_{(x,y)\to (0,0)} ...
2
votes
1answer
133 views

How can I calculate a limit with a free variable?

For example, when I evaluate Limit[(1 + x^n + (x^2/2)^n)^(1/n), n -> Infinity] Mathematica does not output any result. When I evaluate ...
0
votes
1answer
1k views

Given x[u,v], y[u,v], and f[x,y] how do I find D[f,x] in terms of u,v?

I have two functions x = x(u,v) and y = y(u,v). The chain rule says that for a function f(x,y), df/dx = df/du du/dx + df/dv dv/dx, and similarly df/dy = df/du du/dy + df/dv dv/dy. How do I get ...
9
votes
3answers
2k views

How can I differentiate Numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
2
votes
1answer
276 views

About high dimensional integrals

I want to be able to do high dimensional integrals like, (..naively I wrote it as this..) ...
8
votes
1answer
303 views

ReplaceAll[] and Limit[] don't give correct results for this expression under extreme variables [duplicate]

Possible Duplicate: Funny behaviour when plotting a polynomial of high degree and large coefficients 1/x^2 + (3 + x)/(6 (1 - Exp[x] + x)) ——This is a ...
1
vote
1answer
115 views

How to explain the results of the following integrals?

Why does the following program lead to different results of a21 and a211? ...
17
votes
5answers
5k views

How to find the domain and range of a function with Mathematica?

I'm studying calculus and in some exercises I am asked to find the domain and range of a function. Does Mathematica have already a built-in function for this? I can imagine some ways of doing so, ...
8
votes
3answers
572 views

Inverting a function in a certain region

InverseFunction works well for globally invertible functions, like f = 2*# + 2 &; InverseFunction[f] ...