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Signed-off-by: Silvio Fanzon <silvio.fanzon@gmail.com>
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sfanzon committed Sep 17, 2024
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Expand Up @@ -85,9 +85,11 @@ Times and venues are as follows:
- **Lecture 2**: Friday 16:00-18:00 in Wilberforce Building - Lecture Room 16

- **Tutorial**: Time and venues as follows
* Week 1-4: Friday 9:00-10:00 in Larkin Building - Seminar Room 121
* Week 5: Thursday 15:00-16:00 in Larkin Building - Seminar Room 121
* Week 6-12: Friday 9:00-10:00 in Larkin Building - Seminar Room 121
* Week 1-3: Friday 9:00-10:00 in Larkin Building - Seminar Room 121
* Week 4: Thursday 15:00-16:00 in Larkin Building - Seminar Room 121
* Week 5: Friday 9:00-10:00 in Larkin Building - Seminar Room 121
* Week 6: Thursday 15:00-16:00 in Larkin Building - Seminar Room 121
* Week 7-12: Friday 9:00-10:00 in Larkin Building - Seminar Room 121

Please check on MyTimetable every week to see if there are any changes to the following session times and rooms.

Expand Down Expand Up @@ -152,8 +154,8 @@ The module Lecture Notes are available **[here](https://www.silviofanzon.com/202
| 4 | 03/10/24 | 16:00 - 18:00 | Arc-Length. Examples. Scalar product in $\mathbb{R}^2$: geometric definition. SP in coordinates and in $\mathbb{R}^n$. Bilinearity, Symmetry, Differentiation of SP. |
| 5 | 04/10/24 | 09:00 - 10:00 | Speed. Reparametrizations. Regular and singular points. Unit speed reparametrization. Thm: Regularity is equivalent to existence of unit speed reparametrization. |
| 6 | 04/10/24 | 16:00 - 18:00 | Theorem: Arc-length as unit speed reparametrization. Periodic curves. Closed curves. Period of a closed curve. Theorem: Period of closed curve exists. Examples. |
| 7 | 10/10/24 | 16:00 - 18:00 | Curvature: motivation with Taylor formula. Curvature for unit speed curves. Curvature of circle of radius $R$ computed via reparametrization to unit speed curve. |
| 8 | 11/10/24 | 09:00 - 10:00 | Vector Product in $\mathbb{R}^3$: Algebraic definition and geometric properties. General formula for curvature of regular curves (no proof for now). Examples. |
| 7 | 10/10/24 | 15:00 - 16:00 | Curvature: motivation with Taylor formula. Curvature for unit speed curves. Curvature of circle of radius $R$ computed via reparametrization to unit speed curve. |
| 8 | 10/10/24 | 16:00 - 18:00 | Vector Product in $\mathbb{R}^3$: Algebraic definition and geometric properties. General formula for curvature of regular curves (no proof for now). Examples. |
| 9 | 11/10/24 | 16:00 - 18:00 | Plane curves. Signed curvature (SC). Geometric meaning of SC. SC characterizes plane curves (no proof). Correction of Homework 1. |
| 10 | 17/10/24 | 16:00 - 18:00 | Hyperbolic functions and their properties. Example of the catenary curve. |
| 11 | 18/10/24 | 09:00 - 10:00 | Torsion for unit speed curves. Torsion, general formula. Example of calculation of curvature and torsion. Frenet Frame. Frenet-Serret equations. |
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