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0
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1answer
139 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 ...
0
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0answers
147 views

How can I show that a given system of differential equations is stiff?

I was writing a program to solve a system of equations with Runge-Kutta method, but it doesn't work well and I decided to check what Mathematica can say about it. It turns out that I have a stiff ...
3
votes
1answer
192 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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2answers
1k views

How to draw a family of curves and its envelope?

Given a family of curves $$F=(x-t)^2+y^2-\frac{1}{2}t^2,$$ I am trying to compute the envelope of this family. The envelope is described by the equations $$F=0, \\ \dfrac{\partial F}{\partial t} ...
1
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0answers
232 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
177 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
191 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
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1answer
64 views
0
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1answer
112 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
62 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
vote
5answers
748 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
208 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
150 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
597 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
169 views

Precision and time of calculating the integral in Mathematica

1)How to calculate this integral, because I have some very small values (10^-20) in solution and values on this position in matrix should be equal to zero. If I can not do that with working precision, ...
2
votes
1answer
406 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
vote
1answer
189 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
4k 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
444 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
236 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
383 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
424 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
360 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
438 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
711 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
vote
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
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
1
vote
1answer
89 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
288 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: ...
-3
votes
1answer
267 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
389 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
595 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
602 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
910 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
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
votes
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
votes
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] ...
1
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1answer
430 views

Possible bug in Mathematica?

I'm running Mathematica 7.0.0 and came across this weird calculation (lines 1-14). ...
1
vote
2answers
155 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 ...
0
votes
2answers
272 views

How to solve this equation in Mathematica

How do I solve this equation in Mathematica? Using the NSolve command doesn't work! ...
0
votes
1answer
272 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 $$ ...
0
votes
1answer
71 views

A function of two functions that loses dependence on an argument

Say I have two functions: f[a_,b_]:=a + b g[c_,d_,e_]:=c + d - e And I define a third function: ...
0
votes
2answers
125 views

Create list of {x,f(x)} pairs

How can I do this in Mathematica: r=Range[0,20,0.13]; fr = HeavisideTheta[r]; data = somecoolfunctionsinmathematica[r,fr] So that data now is in the form useful ...
1
vote
1answer
170 views

Plotting a Function

How can one plot a three-dimensional plot of a differential equation system of the following to show the trajectories in mathematica: $x' = yz,~ y' = -2xz,~ z' = xy$ I tried using ...
2
votes
0answers
388 views

Calculate periodicity in 1-dimensional array with noise

I have a 1-dimensional array with some integers, which are periodically increasing. Something like this (1 period here): ...