User:Danenberg

From Wikisophia

Contents 1 Provenance 2 Officium 3 Sandbox 3.1 Direction field 3.2 Vector field 3.3 Tangent planes 3.3.1 Falling leaf 3.3.2 Anti-intuition 3.4 Linear independence 3.4.1 Problem 3.4.2 Wronskian 3.4.3 Solution 3.5 Clairaut's Theorem 3.6 Violent curiosity 3.7 Partial derivatives 3.8 Limit 3.9 Family of curves 3.10 Curve with contour 3.11 Erotic paraboloid 3.12 Osculating cirles 3.13 Tangent, normal, binormal 3.14 Curvature of e 3.15 <t, t², t³> ∩ <sin(t), sin(2t), t> 3.16 Cylinder ∩ paraboloid 3.17 Co-sinusoidal demi-toroid 3.18 Toroidal spiral 3.19 Orthogonal matrices 3.19.1 Problem 3.19.2 Inverse matrix 3.19.3 Solution 3.20 Surfaces 3.21 Fugale Gelehrtheit 4 See Also

[edit] Provenance

Of Gens Danenbergorum; Peter Charles Danenberg, Jr.

[edit] Officium

MediaWiki Development; namely WikiTeX

[edit] Sandbox

[edit] Direction field

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

[edit] Vector field

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

[edit] Tangent planes

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

[edit] Falling leaf

[edit] Anti-intuition

[edit] Linear independence

[edit] Problem

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

[edit] Wronskian

[edit] Solution

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

[edit] Clairaut's Theorem

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

[edit] Violent curiosity

Tangent at a point of plane-ellipsoid intersection:

[edit] Partial derivatives

[edit] Limit

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

[edit] Family of curves

[edit] Curve with contour

[edit] 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

[edit] Osculating cirles

[edit] Tangent, normal, binormal

[edit] Curvature of e

[edit] <t, t², t³> ∩ <sin(t), sin(2t), t>

[edit] Cylinder ∩ paraboloid

[edit] Co-sinusoidal demi-toroid

[edit] Toroidal spiral

[edit] Orthogonal matrices

[edit] Problem

[edit] Inverse matrix

[edit] Solution

[edit] Surfaces

[edit] Fugale Gelehrtheit

[Listen]

[edit] See Also

• http://en.wikipedia.org/wiki/User:Danenberg
• http://meta.wikipedia.org/wiki/User:Danenberg
• http://caturanga.org/wiki/Benutzer:Danenberg