From a82759411305d2e8d3e98a1d93eab2ffbbb75697 Mon Sep 17 00:00:00 2001 From: Silvio Fanzon Date: Tue, 17 Sep 2024 15:04:33 +0100 Subject: [PATCH] Signed-off-by: Silvio Fanzon --- _posts/2024-09-15-Differential-Geometry.md | 12 +++++++----- 1 file changed, 7 insertions(+), 5 deletions(-) diff --git a/_posts/2024-09-15-Differential-Geometry.md b/_posts/2024-09-15-Differential-Geometry.md index fc1496d5020f..1f7c9ff6d959 100644 --- a/_posts/2024-09-15-Differential-Geometry.md +++ b/_posts/2024-09-15-Differential-Geometry.md @@ -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. @@ -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. |