Elementary Global Differential Geometry (MAE624): Διαφορά μεταξύ των αναθεωρήσεων

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=== Attached Bibliography ===
=== Attached Bibliography ===


See [https://service.eudoxus.gr/public/departments#20 Eudoxus]. Additionally:
See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Additionally:
* Barrett O' Neil, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
* Barrett O' Neil, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
* Manfredo do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976
* Manfredo do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976

Αναθεώρηση της 10:50, 26 Ιουλίου 2022

Undergraduate Courses Outlines - Department of Mathematics

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAE624

Semester

6

Course Title

Elementary Global Differential Geometry

Independent Teaching Activities

Lectures (Weekly Teaching Hours: 3, Credits: 6)

Course Type

Special Background

Prerequisite Courses -
Language of Instruction and Examinations

Greek

Is the Course Offered to Erasmus Students

Yes (in English)

Course Website (URL) -

Learning Outcomes

Learning outcomes

It is an introductory course on global differential geometry. The aim is to study global geometric properties of regular plane curves and regular surfaces. The study requires tools from Linear Algebra, Calculus of several variables, Topology and elementary differential geometry. On completion of the course the student should be familiar with the interplay between local and global properties of curves and surfaces.

General Competences
  • Work autonomously
  • Work in teams
  • Develop critical thinking skills

Syllabus

Convex curves, Hopf's Umlaufsatz, Four vertex theorem, isoperimetric inequality. Surfaces, vector fields, covariant derivative, parallel transport, geodesic curvature, geodesics, exponential map, surfaces of constant Gaussian curvature, Gauss Bonnet Theorem, Liebmann Theorem.

Teaching and Learning Methods - Evaluation

Delivery

Direct

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 39
Autonomous study 111
Course total 150
Student Performance Evaluation

Written final examination

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Additionally:

  • Barrett O' Neil, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
  • Manfredo do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976