For questions concerning the popular computational software program published by Wolfram Research. (Note: you are more likely to get quicker and more accurate response if you ask the question on their user forum or on the Mathematica StackExchange site.)

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1answer
172 views

Solve autonomous ODE with Mathematica

I'm given a problem with the ODE y'[x]=y[x]*Sqrt[4-2y[x]] I've tried DSolve[{w'[x] == w[x]*Sqrt[4 - 2*w[x]]}, w[x], x] which gives me {{w[x] -> -2 (-1 + Tanh[1/2 (-2 x - Sqrt[2] C[1])]^2)}} but ...
1
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2answers
2k views

How to solve transcendental equations with Mathematica 7?

I want to solve transcendental equations by Mathematica 7. Solve does not help me, reduce - as well. Seams that I shoulkd use FindRoot, but it does not give all solutions. It gives only one solution. ...
2
votes
3answers
54 views

A way to identify a unique number '$a_1$' has performed operations on '$x$'

The problem I have is bit vague, so I will try to explain as best as I can. Suppose we have a base number '$x$' and a set of unique number $'a_1', 'a_2', 'a_3', 'a_4'$ and so on Now $a_1$ perform ...
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5answers
584 views

Cryptography in Maple and Mathematica

Is Maple or Mathematica preffered over the other for Cryptography/Number Theory? What are the advantages for each in terms of this area of mathematics? Also could someone compare and contrast ...
3
votes
1answer
704 views

Solution to a second order semilinear elliptic PDE

I am trying to find a solution (if one exists) to this PDE where (r,z) are cylindrical coordinates. $$u_{rr}+u_{zz}+u_{r}/r-u/r^2 = u^2u_{r}/r+u(u_{r})^2+u(u_z)^2$$ u is a dimensionless function ...
2
votes
1answer
230 views

Two questions on integration of $\operatorname{sech}x$, one with Mathematica

So I have a two fold question, one I believe is simple but my algebra seems to be off, the other involves the trapezoidal rule of integration using Mathematica as an aid. Here they are: $1.\quad ...
1
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1answer
1k views

Help with the Neumann boundary conditions

The Mathematica code is here. Consider the heat conduction problem with Neumann (constant flux) at both boundaries of a solid slab. A constant radiant heat flux is imposed on one surface (derivative ...
1
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1answer
946 views

Existence of non-trivial solution of Sylvester equation.

I'm trying to solve a special case of Sylvester equation in my case it looks like $$A*X=X*B$$ so it can be written in form $$A*X+X*(-B)=C$$ where C consist of all 0 items. I tried to solve it in ...
6
votes
3answers
306 views

Computer Algebra Systems which implement Cylindrical Algebraic Decomposition

My understanding is that Mathematica's Reduce function is based on Cylindrical Algebraic Decomposition (CAD). The only other system I've seen which implements CAD ...
0
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1answer
153 views

Using a Bivariate Gaussian Distribution to Predict Range of Movement

I am currently attempting to use a bivariate normal distribution to identify the most likely range of movement for a blob in computer vision. This itself is not the problem, however; I do not ...
2
votes
1answer
349 views

Closed form with of a series Mathematica

I've these two series, and I would like a closed form: $$ \sum_{k=-\infty}^{\infty} \frac{x+kx_0-h}{|x+kx_0|^3}$$ $$ 3\sum_{k=-\infty}^{\infty} \frac{(x+kx_0-h)(x+kx_0)^2}{|x+kx_0|^5} $$ ...
3
votes
0answers
142 views

Perturbation problem

This is a mathematica exercise that I have to do, where $y(x) = x - \epsilon \sin(2y)$ and it wants me to express the solution $y$ of the equation as a power series in $ \epsilon$.
4
votes
4answers
9k views

How do I convert the distance between two lat/long points into feet/meters?

I've been reading around the net and everything I find is really confusing. I just need a formula that will get me 95% there. I have a tool that outputs the distance between two lat/long points. ...
0
votes
1answer
150 views

Euler's Numerical method help

Consider this differential equation, $dy/dx = x + \sin(y)$ with initial condition $y = 0.5$ when $x = 1.2$: Write down the recurrence relation for Euler's numerical method ...
3
votes
1answer
560 views

Method For Constructing Self Referential Formulas Like Tupper's

Can anyone please explain exactly how formulas like Tupper's self referential formula can be constructed? I'll like to see the reasoning behind the derivation of such formulas and the steps required ...
1
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0answers
236 views

(Improved; Kindly assist )CSI Forensic Maths

In a square room with 7 m-long sides, five people have shot at random people. They all had two bullets and killed two people in the crowd. Other people in the room were not hurt. CCTV recordings show ...
1
vote
1answer
181 views

Expanding squares and simplification of equations

as i'm reading a paper "An Underdetermined Linear System for GPS" By Dan Kalman i understand the paper but when i traced the equations there's something i don't understand ,may be my mathematics is ...
0
votes
2answers
217 views

Integrating with vector coefficients in Maple

I'm trying to use Maple to do something like this integral: $\displaystyle\int \frac{a\mu-b}{||a\mu-b||^3} \mathrm{d}\mu$ Where $a, b$ are vectors and $\mu$ is a scalar I'm integrating by. But I ...
0
votes
1answer
65 views
0
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1answer
122 views

How to find a parametrization of a equation and to draw its picture.

I was wondering how to find a parametrization of $(x-t)^2+(y-t^2)^2-t^2=0$, and how to use a software like Mathematica to draw a picture of this equation based on the parametrization. Thanks in ...
1
vote
1answer
66 views

can't figure out what I been doing wrong on simple integration question

$$\int_0^1 \sqrt{(\sqrt{5})^2+(2t)^2}\;dt$$ Based on the formula $\int \sqrt{a^2+x^2}\;dx=\frac{1}{2}[x\sqrt{a^2+x^2}+a^2\log(x+\sqrt{a^2+x^2})]$ I just plug in above input into the formula above ...
1
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5answers
806 views

Numerical solution in Matlab or any other solver

I need to find x of this equation: 1.0221044505936159^x + 1.0446975079232772^x + 1.0677899723724409^x + 1.091392883061106^x + 1.1155175231229544^x + 1.140175425099138^x + 1.1653783764512973^x + ...
1
vote
2answers
210 views

Help need in Mathematica or Sage

I want to find the common positive solutions of two polynomials $f_{a,b}(x,y)$, $g_{a,b}(x,y)$ where $a,b$ runs from 0 to 1 with an interval 0.01. Let $(x_0,y_0)$ be a common positive solution. Then ...
0
votes
1answer
151 views

How could calculate this definite integral by mathematica software

I have a expression given as $F=f_1(x)+f_2(x)+\cdots+f_N(x)$ Now I want to simplify this integral as FullSimplify[$\int \limits_0^\infty F \;dx$]. It takes along time to calculate. If I factor it into ...
0
votes
1answer
91 views

Solving a one line matrix, constraining the coefficients

I will give a simple example of my question then the full one. Let's say I am trying to reconcile my bank account, and have no statement. I opened it with $0 exactly, and a small number of ...
2
votes
2answers
655 views

Finding root of a polynomial

Let's say I've got $ax^3 + bx^2 + cx + d = 0$ I want to find x for a general-case. Mathematica gave me a very long solution, and even longer for one which has $kx^4$. Can you please help me ...
4
votes
3answers
2k views

Is it A Good Idea To Write Papers With Mathematica?

I find it very easy to write with mathematica. There are a lot of templates to choose from, and the formula visualization is cool. Also it's very convenient to manage chapters and sections. With ...
2
votes
1answer
431 views

Symbolic computation of the derivative of dot product of 2 vectors

If I have two vectors $a$ and $b$, whose components are time varying, for example $$a=[a_x(t), a_y(t), a_z(t)]$$ $$b=[b_x(t), b_y(t), b_z(t)]$$ The dot product of these 2 vectors can be expressed as ...
1
vote
1answer
1k views

Mean Residual Life, clarification needed

I had previously posted this question at StackOVerflow but given it seems more about probability than programming I thought this forum mind give it a more suitable environment. I need to understand ...
1
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1answer
198 views

p-norm of series / Mathematica

When computing the $p$-norm of the series $x_n = \mathrm e^{\mathrm i n}$ for $n \in \mathbb{Z}$ (not $\mathbb{N}$), the sum should not converge: $$\|x\|_p^p = \sum_{n \in \mathbb{Z}} (\mathrm ...
0
votes
1answer
5k views

Plot Y-Range on Mathematica

I have a plot that I would like to slightly manipulate in Mathematica. Here is the code I am entering: Plot[{x, 2^x, log_2(x)}, {x, -1, 3}] As you can see $x$, $2^x$, and $log_2(x)$ are all ...
0
votes
1answer
458 views

Q-Test in mathematica

I want to use the Q-test to determine outlier in my dataset. However, I cannot find a function to do this is in Mathematica. Does anyone know if there is a function which does this in Mathematica? ...
0
votes
1answer
278 views

Automated generation of a parametric plot?

Currently we are introducing integrals of manifolds in $3d$-Space in a course. We are given some set $E \subset \mathbb{R}^3$ and should evaluate the surface and scetch how it looks. For example ...
0
votes
2answers
422 views

Ackermann function

I have trouble with a question i need to use the function of Ackermann, I need to show that Ack(2,3) = 9. ...
2
votes
1answer
449 views

Finding General Expression from recursion

I am trying to find a general expression from a recursion. Here it goes: $(x+i)P_i = (i+1)P_{i+1} + \frac{x}{2} P_{i-1}$ $i$ goes from $0$ to $S$. How can I calculate a generic $P_i$ in terms of ...
6
votes
4answers
376 views

Best tool for verifying algebraic manipulations

Can anyone advise a tool that is very convenient for verifying algebraic manipulations step by step as I work. I too often waste hours dealing with a wrong formula because I missed a sign somewhere. I ...
2
votes
1answer
459 views

How to use Mathematica to solve equations in a polynomial ring?

I am sorry. But I wonder whether it is fine to ask this question here. I need some help to solve some equations in a polynomial ring: Give the ring $\mathbb{F}_p [x ]/(x^2+x+1)$, where $p$ is a ...
1
vote
3answers
834 views

How to plot $z= 5-\sqrt{x^2+y^2}, 0 \le z \le 5$ in mathematica?

Could anybody tell me how to plot $z= 5-\sqrt{x^2+y^2}, 0 \le z \le 5$ in mathematica? I haven't done much on multivariable yet, but I am inquisitive to know how to plot this cone on mathematica? ...
1
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1answer
4k views

Error When Using Mathematica To Solve Differential Equation

I have a concern of why mathematica does not like/except the independent variable x. When it is used it gives the following error: In[1]:= DSolve[{2 x''[t] + ...
1
vote
1answer
71 views

Finding the fit $A\ T^a+B\ T^{-b}\ \rightarrow\ C\ T^c\exp{(\small{-\frac d T})}$ for an interval? (specifically in Mathematica)

I'm given an expression $$A\ T^a+B\ T^{-b},$$ $$\text{with} \ \ \ \ A,B>0,\ \ \ \ a,b\in(0,1),$$ but the plus sign "$+$" is a problem for my purposes. I want to make a fit of the following ...
0
votes
1answer
69 views

Help Plotting in Mathematica

I have a function of the form S=f(x,y,z), 0 ≤ x ≤ 1,0 ≤ y ≤ 1, 0 ≤ z ≤ 1. I would like to solve S=0 numerically and plot the solution set of (x,y,z) in 3-space
1
vote
1answer
90 views

See currently assigned variables in Mathematica

I've noticed that in a notebook, if I define a variable, and then delete the definition, the variable stays assigned. Is there a quick way to see all the variables that are assigned? I can find them ...
7
votes
4answers
1k views

Drawing a thickened Möbius strip in Mathematica

I would like to have Mathematica plot a "thickened Möbius strip", i.e. a torus with square cross section that is given a one-half twist. Ideally, I would like this thickened Möbius strip to be ...
2
votes
3answers
325 views

What is the analytic form of MeijerG in Mathematica?

I know that the official standard formula can be found here, but I am having a very hard time simplifying this special case: ...
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votes
1answer
295 views

How to solve this integral of trigonometric f in Mathematica

How to solve this integral in Mathematica Is it possible to solve it numerically? $$\begin{align} \int_{-1}^1 \cos\big(&(.75-.75x^2)\cdot y_1 + (.25 - .5x - .75x^2) \cdot y_2 \\ + &(-.5x ...
1
vote
2answers
434 views

Transcendental Equations, Matrix (Eigenvalue problem?) (Mathematica)

I'm currently having trouble getting my head around solving this matrix (eigenvalue problem?) transcendental equation. I have a matrix 4x4 where, $\det(M)=0$. And where ij of the matrix is a ...
2
votes
1answer
623 views

Fourier transform in Mathematica

When I calculate the Fourier transform of the function $$f(t) = \mathrm e^{-|t|/\tau} \text{ with } \tau >0$$ in Mathematica once via the function FourierTransform and once by hand, I get different ...
2
votes
2answers
664 views

How to obtain Eigenvalues with maximum precision in Mathematica

One short question. If we have two matrices in fractional form, how to obtain the Eigenvalues[{A,B}] with maximum precision or get it also in fraction form?
6
votes
1answer
992 views

Solution of a system of equations in a finite field using Mathematica

We can solve a system of equations over reals using Mathematica as follows. Solve [x^2+y^2+z^2==1 && x+y==1, {x,y,z}] How one can solve a system of ...
4
votes
1answer
1k views

Why Mathematica (Reduce) can't find clear solution for almost trivial inequalities?

Suppose we want to solve the inequality $ax^2+bx+c<0$. For simplicity, presume that $a>0$ and $b^2-4ac>0$. In this form, this is almost a trivial problem. Despite that, if we want to solve it ...