Geometry
Summary
The course provides an introduction to the study of curves and surfaces in Euclidean spaces. We will learn how we can apply ideas from differential and integral calculus and linear algebra in order to "measure shapes".
Content
Topics to be covered in this course include:
- tangent vectors, vector fields, moving frames
- planar and space curves and their geometric properties
- surfaces and notions of curvature
- (Euclidean) isometries
Learning Prerequisites
Required courses
Analysis I, Linear Algebra
Important concepts to start the course
Fundamental notions from differential and integral calculus and linear algebra.
Learning Outcomes
By the end of the course, the student must be able to:
- Link concepts from calculus to geometric properties of curves and surfaces
- Describe relevant examples of curves and surfaces
- Visualize geometric transformations in the plane and in three-dimensional space
- Carry out a range of computations which may be applicable to engineers
- Demonstrate effective use of fundamental notions involving curves and surfaces
Teaching methods
Lectures and exercise classes.
Assessment methods
Written exam.
Supervision
| Office hours | No |
| Assistants | Yes |
| Forum | No |
Resources
Bibliography
The following are good books which are also available through the EPFL library:
- (English translation) Differential Geometry of Curves and Surfaces by S. Kobayashi.
- (English translation) Differential geometry of curves and surfaces by M.P. do Carmo.
- (In French) Cours de géométrie by M. Troyanov.
- (Chapter 3) Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers by H. Nguyen-Schäfer and J-P Schmidt.
- (Chapters 19 and 20) Geometric Methods and Applications: For Computer Science and Engineering by J. Gallier.
Ressources en bibliothèque
- Differential Geometry of Curves and Surfaces / Kobayashi
- Differential geometry of curves and surfaces / de Carmo
- Cours de géométrie / Troyanov
- Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers / Nguyen-Schäfer
- Geometric Methods and Applications / Gallier
Notes/Handbook
There will be (handwritten) lecture notes.
Moodle Link
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Geometry
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks