Week | Date | Reference | Topics |
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1 | Monday 1/27/2020 |
Notes: Chapters 1, 2 |
Euclidean geometry Cartesian coordinates Abstract vector spaces |
Wednesday 1/29/2020 |
Axler: Chapters 1, 2 Notes: Chapter 3 |
Abstract vector spaces Linear indepdendence Linear basis Linear maps |
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2 | Monday 2/3/2020 |
Notes: Chapter 4 |
Affine spaces Affine independence Affine basis Affine maps |
Wednesday 2/5/2020 |
Notes: Chapter 6 O'Neill: Chapter 3 |
Affine and vector space versions of \(\mathbb{R}^m\) Inner product on a vector space Euclidean space |
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3 | Monday 2/10/2020 |
Notes: Chapter 7 O'Neill: Sections 2.1-2.3 |
Curves in Euclidean space Velocity, speed, acceleration Curvature of a curve in Euclidean 2-space Frenet-Serret frame and equations in Euclidean 2-space |
Wednesday 2/12/2020 |
Notes: Chapter 7 O'Neill: Sections 2.3-2.4 |
Frenet-Serret frame and equations in Euclidean 2-space | |
4 | Monday 2/17/2020 |
No class, Presidents' Day | |
Wednesday 2/19/2020 |
Notes: Section 7.2 O'Neill, Chapter 4 |
Curvature, torsion of a curve in Euclidean 3-space Frenet-Serret frame and equations in Euclidean 3-space Curvature and torsion imply uniqueness up to rigid motion |
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5 | Monday 2/24/2020 |
Notes: Chapter 8 and 9 O'Neill: Sections 4.1-4.2 |
Definitions of a surface in \(\widetilde{\mathbb{R}}^3\) |
Wednesday 2/26/2020 |
Notes: Chapter 9 O'Neill: Section 4.3 |
Coordinate charts Sphere Torus Tangent space |
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6 | Monday 3/2/2020 |
Notes: Chapter 10 O'Neill: Chapter 1 |
Tangent space First fundamental form |
Wednesday 3/4/2020 |
Notes: Chapter 10 O'Neill, Chapter 1 |
First fundamental form |
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7 | Monday 3/9/2020 |
Geometry of curve in surface in \(\mathbb{E}^3\) Second fundamental form Gauss map |
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Wednesday 3/11/2020 |
Notes: Chapter 10 |
Dual vector space Dual basis Natural isomorphism \(V^{**}\simeq V\) Directional derivative Differential of function |
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3/16/2020, 3/18/2020 | No class, Spring Recess | ||
8 | Monday 3/23/2020 |
O'Neill, Chapter 4 |
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Wednesday 3/25/2020 |
O'Neill, Chapter 4 |
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9 | Monday 3/30/2020 |
O'Neill, Chapter 4 |
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Wednesday 4/1/2020 |
O'Neill, Chapters 4 |
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10 | Monday 4/6/2020 |
O'Neill: Chapters 2 and 6 |
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Wednesday 4/8/2020 |
O'Neill: Chapter 2 |
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11 | Monday 4/13/2020 |
O'Neill: Chapter 6 |
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Wednesday 4/15/2020 |
O'Neill: Chapter 6 |
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12 | Monday 4/20/2020 |
O'Neill: Section 3.3 |
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Wednesday 4/22/2020 |
O'Neill: Chapter 4 |
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13 | Monday 4/27/2020 |
O'Neill: Chapter 4 |
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Wednesday 4/29/2020 |
O'Neill: Chapters 4 and 6 |
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14 | Monday 5/4/2020 |
O'Neill: Chapters 4 and 7 |
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Wednesday 5/6/2020 |
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15 | Monday 5/11/2020 |
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