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

Lire la suite

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

• https://go.epfl.ch/MATH-123_b