Snapshots, whiteboard scans, and notes

2011 all months

2012 March 6

  • examples of separable non-separable metric sets (Def1.5 p2 and implications on p.5)
  • continuity in terms of open sets. (Def1.7 p.2)
  • Ex.1.9.2, 3
  • Linearization of a map by its total derivative, (p.3 starting "The associated linear map...")
  • work through p.4
  • show what exactly went wrong with the spaces in Remark 2.2.4

2012 March 13

  • Linearization of maps, chain rule, Ex 1.14, 1.15, 2.3

2012 March 20

  • Linearization of maps, chain rule, Ex 1.14, 1.15, 2.3

2012 March 27

  • Linearization of maps, chain rule, Ex 1.14, 1.15, 2.3
  • Understanding Inverse function theorem in terms of $Df$
  • bijection, homeo-, diffeo-morphism definitions

2012 April 03

  • Inverse function theorem Thm 1.16
  • bijection, homeo-, diffeo-morphism definitions and Cor1.17
  • Ex.1.18 of (local) diffeomorphisms
  • Thm 1.18 of flow map

2012 April 17

  • Section summary, Ex. 1.20
  • Gunter used Ex. 1.20.1 as an example of non-separable set in a given metric?

2012 April 24

  • Sub-multiplicative operator norm
  • Ch.2 Differentiable Manifolds, Def 2.1, Remarks 2.2
  • Ex 2.3.1

2012 May 01

  • Ex. 2.3.2
  • Ex. 2.3.3

2012 May 08

  • Def 2.4
  • Prop 2.5

2012 May 15

  • Def 2.4 again
  • Hyperbolic geometry

2012 May 22

  • Regular value and regularity theorem
  • Ex 2.9
  • 2.10

Ch2

  • Exercises to Ch 2

Exterior algebra

  • Exterior algebra

2012 November-December

  • Chen-Yang's problem
  • Maxwell equations
  • Frankel Ch3. Integration of diff. forms
  • Maxwell equations: energy conservation

Return to differential geometry study group

When $a \ne 0$, there are two solutions to $ax^2 + bx + c = 0$ and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$