The infinitesimals tag has no wiki summary.

**-2**

votes

**0**answers

25 views

### simplifying an equation that has infinitesimals [on hold]

I'm trying to understand an equation with infinitesimal changes:
8*X*dX = d(4*X^2)
I think this can be written
$8X\Delta X = \Delta (4(X^{2}))$
I'm guessing going from 8 outside the differential ...

**1**

vote

**0**answers

52 views

### Obtaining graphics of functions in non-standard analysis

In the context of $R(\varepsilon)$ or more broad fields, Levi-Civita field or $No(\omega_1)$, how can we obtain the graphics of functions on the infinitesimal range?
For instance, it is alleged that ...

**3**

votes

**0**answers

154 views

### Analysing functions on zero-length intervals and super-small values

Suppose a function that has a pole in $x=0$:
Here we see the graphic of the real part of the Gamma function.
As we can see on it, there is a vertical line at $x=0$ that comes from $-\infty$ to ...

**16**

votes

**2**answers

633 views

### Felix Klein on infinitesimals

This is a reference request prompted by some intriguing comments made by Felix Klein.
In 1908, Felix Klein formulated a criterion of what it would take for a theory of infinitesimals to be ...

**3**

votes

**2**answers

295 views

### Is there a source linking Robinson's work in wing theory with his theory of infinitesimals?

Abraham Robinson worked in applied mathematics for several decades. MathSciNet lists 12 articles by Robinson in wing theory. His production included the book
Robinson, A.; Laurmann, J. A. Wing ...

**1**

vote

**1**answer

163 views

### Can elements of Weil algebras be detected by maps into truncated symmetric algebras?

Recall that a Weil algebra is a finite-dimensional real unital algebra that admits exactly one homomorphism to R.
Such algebras form the basis of the Weil approach to differential geometry, pioneered ...

**7**

votes

**3**answers

794 views

### Nontrivial trivial integrals

I posted this question to stackexchange and after 24 hours it's got five votes and no answers, so let's see if mathoverflow can say more than that.
Consider two propositions in geometry:
...