User:Danenberg

From Wikisophia

Provenance

Of Gens Danenbergorum; Peter Charles Danenberg, Jr.

Officium

Sandbox

Direction field

Reproduced from William E. Boyce and Richard C. DiPrima, Elementary Differential Equations and Boundary Problems (Hoboken: John Wiley, 2005), 35.

Vector field

Gradient vector field of along with its contour map, courtesy of a beautiful hack by Thomas Sefzick.

Tangent planes

At increasing levels of detail, the surface approaches its tangent plane around P.

Falling leaf

Anti-intuition

Linear independence

Problem

If for , show that is linearly independent on every interval for all fixed .

Wronskian

Solution

has a non-zero Wronskian on ; and is therefore linearly independent on that interval.

Clairaut's Theorem

That does not contradict Clairaut's Theorem , where and are permuted indices of with replacement, since and are not continuous.

Violent curiosity

Tangent at a point of plane-ellipsoid intersection:

Partial derivatives

Limit

That--doesn't-exist's graphical representation.

Family of curves

Curve with contour

Erotic paraboloid

Context from #math on freenode:

00:57 <klutometis> I've come up with a new nomination: the "erotic
                   paraboloid"
00:57 <klutometis> http://wikisophia.org/wiki/User:Danenberg#Erotic_paraboloid
00:58 <thermoplyae> you appear to have a lot of free time
00:59 <klutometis> thermoplyae: me? it corresponds roughly with calculus;
                   so no expenditure of free time
00:59 <TRWBW> klutometis: hehe, n1, something just like it at
              http://www.youtube.com/watch?v=eBGIQ7ZuuiU
01:00 <thermoplyae> you say that, but all the busy people i know don't draw
                    graphs of "co-sinusoidal demi-toroid"s
01:00 <klutometis> damn it, TRWBW; I can't believe I got rick rolled
01:00 <thermoplyae> just sayin'
01:00 <thermoplyae> haha
01:01 <klutometis> thanks, boys; good night