Elementary Differential Geometry (MAY522): Διαφορά μεταξύ των αναθεωρήσεων

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


* Δ. Κουτρουφιώτης, Στοιχειώδης Διαφορική Γεωμετρία, Εκδόσεις Leader Books, 2006
See [https://service.eudoxus.gr/public/departments#20 Eudoxus]. Additionally:
* Barrett O' Neil, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
* Barrett O' Neil, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
* Andrew Pressley, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2011
* 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 22:15, 21 Ιουλίου 2022

Undergraduate Courses Outlines - Department of Mathematics

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAY522

Semester 5
Course Title

Elementary differential geometry

Independent Teaching Activities

Lectures (Weekly Teaching Hours: 5, Credits: 7.5)

Course Type

General Background

Prerequisite Courses -
Language of Instruction and Examinations

Greek

Is the Course Offered to Erasmus Students

Yes (in English)

Course Website (URL)

http://users.uoi.gr/tvlachos/

Learning Outcomes

Learning outcomes

It is an introductory course on differential geometry. The aim is to introduce and study geometric properties of regular curves (both plane and space) and regular surfaces. Fundamental notions of differential geometry of curves and surfaces are introduced and studied. Among them is the notion of curvature. The study requires tools from Linear Algebra and Calculus of several variables.
Upon completion of the course, the student should be familiar with basic notions of differential geometry like the one of curvature, first and second fundamental form, isometries between surfaces and their geometric meaning.

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

Syllabus

  • Plane curves, arclength, curvature, Frenet frame.
  • Space curves, curvature and torsion, Frenet frame, fundamental theorem of curves.
  • Surfaces, parametrization, Gauss map, Weingarten map, first and second fundamental form, normal curvature, principal and asymptotic directions, Gaussian and mean curvature, minimal surfaces, Theorema Egregium, Gauss and Weingarten formulas, fundamental theorem of surfaces, developable surfaces.

Teaching and Learning Methods - Evaluation

Delivery

Direct

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 65
Autonomous study 127.5
Course total 187.5
Student Performance Evaluation

Written final examination

Attached Bibliography

See Eudoxus. Additionally:

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