20
votes
Accepted
An efficient way to translate a triple for-loop from Matlab to Mathematica
Okay, let's focus on this snippet:
...
- 109k
18
votes
The Lotka-Volterra predator-prey model
The dimensional phase-space plot
The analysis of the predator-prey model is incomplete without the phase-space plot. So, here it is,
...
- 12k
12
votes
For Loop and Sum
Anyone asking you to write For loops in Mathematica for such a problem is a dolt. Nevertheless, here's how you might do that:
...
- 1,534
11
votes
10
votes
Area of volume of revolution
r = ParametricRegion[{r Cos[ϕ], Sin[ϕ] r,
Sqrt[28 r]}, {{r, 0, 21}, {ϕ, 0, 2 π}}]
Area[r]
49/2 π (14 Sqrt[3] - ArcSinh[...
- 5,189
10
votes
9
votes
8
votes
Accepted
7
votes
Accepted
7
votes
Accepted
Strange determinant result
Det[{{0, 1/v, 0, -k12/v^2},
{0, 0, 0, -1/v^2},
{k12, k01, 0, 0},
{1, 1, 1, 0}}]
(* k12/v^3*)
Laplace
...
- 55.6k
7
votes
Accepted
Analyze stability of equilibria using Routh-Hurwitz conditions
There are "modified Routh-Hurwitz criteria" that work directly on the Jacobian matrix that I prefer and don't seem very well known (Fuller 1968). Here's a function I wrote that uses them for up to ...
- 20.3k
7
votes
How to check whether Laguerre polynomials are orthogonal?
Integrate[LaguerreL[i, x] LaguerreL[j, x] Exp[-x], {x, 0, Infinity},
Assumptions -> Element[{i, j}, Integers] && j > i > 0]
0
...
- 399k
7
votes
Euler's method initial value problem — how should I plot the solution?
Euler's method to solve, plot, and compare to known solution:
$y^\prime = te^{3t}-2y, \quad y(0)=0, \quad 0 \le t \le 1. $
...
- 2,166
7
votes
Adams-Bashforth method implementation code review
There are typos in the code, and after minor correction we have
...
- 47.8k
7
votes
Accepted
Illustrating the central limit theorem
You need to generate 10000 sums of n random numbers and make a histogram of these sums. In your code you just sum up 10000 uniformly distributed random numbers 5 ...
- 629
6
votes
6
votes
Accepted
Rationalize number
Use Minimize with a condition that avoids the divergence to $-\infty$:
Minimize[{f[x], x > 5}, x]
{(-5 + 2 Sqrt[5] +...
- 6,825
6
votes
Accepted
Area of volume of revolution
It seems that f[x] is evaluating to a number. Probably you Set an OwnValues for ...
- 37k
6
votes
Accepted
Infinite While loop
The crux of the matter is how n is changed on each iteration.
Math
Consider a multi-digit integer $n = a_1 a_2 a_3 \ldots a_N$, where $a_k$ is the $k$-th digit of ...
- 7,880
6
votes
How can I animate two beads each sliding on its own frictionless rail?
If there are no restrictions on r, x, then the solution is
...
- 47.8k
6
votes
Find the square root using a recursive formula
Here is an implementation in about as pure a recursive style as you can hope for. It is fully tail-recursive, so it has the same efficiency as an iterative implementation.
...
- 108k
6
votes
6
votes
6
votes
Euler-method implementation
In a functional style, I recommend NestList, the key trick of which is to properly define an iteration function to be used repeatedly via pure/anonymous ...
- 9,873
5
votes
Smiley Face using parametric equations
Couple of non-answers, but I hope interesting.
Chernoff face
So here is another non-answer with a Chernoff face diagram using the package ChernoffFaces.m.
...
- 37.9k
5
votes
Accepted
5
votes
Parametric Curves Tangent Line
x[t_] = t^2 - t;
y[t_] = t^2 + t + 1;
The value of t for the point {0, 3} is
...
- 161k
5
votes
Parametric Curve and Arc Length
You are missing a comma separating the equations from the varied term:
ParametricPlot[{x = Sin[t] + Sin[1.5 t], y = Cos[t]} , {t, 0, 2 Pi}]
Use ...
- 7,515
5
votes
How to find $\delta$ for limit type questions
Here's general way, limited by ability of Reduce to deal with the chosen function:
...
- 241k
Only top scored, non community-wiki answers of a minimum length are eligible