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