Course Information
TitleΚΛΑΣΙΚΗ ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ Ι / Classical Differential Geometry I
Code0303
FacultySciences
SchoolMathematics
Cycle / Level1st / Undergraduate
Teaching PeriodWinter
CommonYes
StatusActive
Course ID40000467

Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 441
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course537

Class Information
Academic Year2019 – 2020
Class PeriodWinter
Faculty Instructors
Weekly Hours5
Class ID
600147631
SectionInstructors
1. ΤΜΗΜΑ ΑPanagiotis Batakidis
2. ΤΜΗΜΑ ΒEfthimios Kappos
Type of the Course
  • Scientific Area
Course Category
Specific Foundation / Core
Mode of Delivery
  • Face to face
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
  • English (Instruction, Examination)
Prerequisites
Required Courses
  • 0301 Analytic Geometry I
  • 0302 Analytic Geometry II
Learning Outcomes
Deeping and understanding of basic concepts of Classical Differential Geometry.
General Competences
  • Apply knowledge in practice
  • Make decisions
  • Work autonomously
  • Work in teams
  • Work in an international context
  • Work in an interdisciplinary team
  • Generate new research ideas
  • Advance free, creative and causative thinking
Course Content (Syllabus)
Theory of Curves: The concept of the curve in the differential geometry. The moving frame. The Frenet formulae. The fundamental theorem (existence and uniqueness). Osculating cycle. Plane curves. Theory of surfaces: The concept of surface in differential geometry. Curves on a surface. The first and the second fundamental form. Gauss, mean curvature and principal curvatures. Christoffel symbols. The Gauss map and equations of Gauss and Weingarten. Theorema Egregium of Gauss. The fundamental theorem (existence and uniqueness).
Keywords
Theory of curves, theory of surfaces
Educational Material Types
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Communication with Students
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures652.2
Reading Assigment1153.8
Tutorial270.9
Exams30.1
Total2107
Student Assessment
Description
Written examination
Student Assessment methods
  • Written Exam with Multiple Choice Questions (Summative)
  • Written Exam with Short Answer Questions (Summative)
  • Written Exam with Extended Answer Questions (Summative)
  • Written Assignment (Summative)
  • Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
- Σ. Σταματάκη: Εισαγωγή στην Κλασική Διαφορική Γεωμετρία, Θεσσαλονίκη, Εκδόσεις Αϊβάζη, 2008 - Ν. Στεφανίδη: Διαφορική Γεωμετρία, Β’ έκδοση βελτ. και επαυξ. Θεσσαλονίκη, 2014 - A. Pressley: Στοιχειώδης Διαφορική Γεωμετρία.Ηράκλειο : Πανεπιστημιακές Εκδόσεις Κρήτης, 2011 - B. O'Neill: Στοιχειώδης Διαφορική Γεωμετρία, Ηράκλειο : Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
Additional bibliography for study
- M. P. do Carmo: Differential Geometry of Curves and Surfaces. Prentice – Hall, 1976 - J. Oprea: Differential Geometry and its Applications. Prentice Hall, 1997 - Β. Παπαντωνίου: Διαφορική Γεωμετρία, Πάτρα : Εκδόσεις Πανεπιστημίου Πατρών, 1996- 1997 - G. Στάμου: Ασκήσεις Διαφορικής Γεωμετρίας. Εκδόσεις Ζήτη, 1990
Last Update
12-12-2019