| |
Mon |
Tue |
Wed |
Thu |
Fri |
Week 1
(Jan) |
Introduction,
Polar Coords
|
|
Motivation,
Dot
&
Cross
|
|
Differential forms,
Higher Rank,
Products
|
Week 2
(Jan) |
Determinants,
Pictures
|
|
Tensors,
Inner Products,
Polar Coords II
|
|
Bases,
Metric Tensor,
Signature
|
Week 3
(Jan) |
MLK Day
|
|
Higher Rank,
Orientation,
Schwarz Inequality
|
|
Hodge Dual,
Euclidean &
Minkowski Spaces,
|
Week 4
(Jan) |
Hodge Dual II,
Dot & Cross,
Pseudovectors
|
|
Gradient,
Exterior Deriv,
Div & Curl
|
|
Gradient,
Exterior Deriv,
Div & Curl
|
Week 5
(Feb) |
Laplacian,
Properties,
Product Rules
|
|
Orthogonal Coords,
Div, Grad, Curl
|
|
Maxwell's Eqs I,
Maxwell's Eqs II,
|
Week 6
(Feb) |
Maxwell's Eqs III
|
|
Review
|
|
Midterm
|
Week 7
(Feb) |
Go over midterm
|
|
Integrals,
Integrands,
Stokes' Theorem
|
|
Stokes' Theorem
Stokes' Corollaries,
|
Week 8
(Feb) |
Spheres,
Topology,
Polar Coords II
|
|
Vector Derivatives
Connections,
|
|
Connections,
Levi-Civita
|
Week 9
(Mar) |
Polar Coords III,
Curves,
Surfaces
|
|
Curvature,
Bianchi Identities
|
|
Geodesic Curvature,
Geodesic Triangles,
Gauss-Bonnet Thm
|
Week 10
(Mar) |
The Torus
|
|
TBA
|
|
Review
|