# Tag Info

Accepted

### An efficient way to translate a triple for-loop from Matlab to Mathematica

Okay, let's focus on this snippet: ...

### 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

### 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: ...

### How to plot trajectories of the Rossler System

You could try NDSolve then ParametricPlot3D ...
• 149k

### 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

...
• 1,950

...
• 161k
Accepted

• 1,081
Accepted

...
• 42.1k
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
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

### 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

### 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

### Adams-Bashforth method implementation code review

There are typos in the code, and after minor correction we have ...
• 47.8k
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

### Implicitly defined curve

First find the y values like Carl Woll proposed. ...
• 17.3k
Accepted

### Rationalize number

Use Minimize with a condition that avoids the divergence to $-\infty$: Minimize[{f[x], x > 5}, x] {(-5 + 2 Sqrt[5] +...
Accepted

### Area of volume of revolution

It seems that f[x] is evaluating to a number. Probably you Set an OwnValues for ...
• 37k
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

### 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

### 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

...
• 241k

### Recreate specific plot in Mathematica

This is a possibility for what you want: ...
• 169

### 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

### 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
Accepted

...
• 161k

### 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