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
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 ...
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1answer
920 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
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3answers
298 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 ...
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1answer
151 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 ...
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1answer
340 views

Closed form with of a series Mathematica

I've these two series, and I would like a closed form: $$ \sum_{k=-\infty}^{\infty} \frac{x+kx_0-h}{|x+kx_0|^3}$$ $$ 3\sum_{k=-\infty}^{\infty} \frac{(x+kx_0-h)(x+kx_0)^2}{|x+kx_0|^5} $$ ...
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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$.
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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. ...
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1answer
143 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
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1answer
345 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 ...
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0answers
235 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 ...
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1answer
180 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 ...
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2answers
214 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 ...
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1answer
65 views
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1answer
119 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 ...
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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 ...
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5answers
782 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 + ...
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2answers
209 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
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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 ...
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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
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2answers
635 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
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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
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1answer
425 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 ...
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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
193 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 ...
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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
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1answer
454 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
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1answer
263 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 ...
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2answers
411 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
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1answer
446 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
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4answers
369 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
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1answer
456 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 ...
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3answers
802 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? ...
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1answer
5k 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] + ...
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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 ...
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1answer
68 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
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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
2k 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
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3answers
313 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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1answer
283 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
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2answers
418 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
618 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
637 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
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1answer
954 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
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1answer
2k 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 ...
2
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1answer
2k views

A series solution of the differential equation: $\frac{d^2u(x)}{dx^2}+ u(x)^n = 0.$

Consider the differential equation $\frac{d^2u(x)}{dx^2}+ u(x)^n = 0.$ Let the solution be $u(x) = u_0(x) + p u_1(x) + p^2u_2(x) + \cdots +p^m u_m(x).$ Now we are interested in substituting the ...
3
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1answer
2k views

Solve a function with sum in Mathematica?

I want to solve an equation with sum in Mathematica, e.g., $$\sum _i \frac{a_i}{x}=1$$ But when I input this: Solve[Sum[Subscript[a, i]/x, i] == 1, x] ...
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1answer
433 views

Possible bug in Mathematica?

I'm running Mathematica 7.0.0 and came across this weird calculation (lines 1-14). ...
1
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2answers
157 views

Taking advantage of linearity of integration in Mathematica

I want to evaluate an integral of form given below $$\int\limits_\alpha^\beta (f(x) + g(x) + h(x) + ...) dx$$ When I give it to Mathematica it takes forever to evaluate. But if I give it in this ...
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2answers
276 views

How to solve this equation in Mathematica

How do I solve this equation in Mathematica? Using the NSolve command doesn't work! ...
0
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1answer
283 views

How to make Runge-Kutta for solving nonlinear ODE system in Mathematica

How to make Runge Kutta method for system of non linear equations in this Matrix form. Matrices A3, B3 and B4 are functions of matrix X3. Initial conditions are X1=X2=X3=X4=0 and system is here $$ ...