Course Information
TitleΔΙΑΦΟΡΙΣΙΜΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ Ι / Differential Manifolds I
Code0304
FacultySciences
SchoolMathematics
Cycle / Level1st / Undergraduate
Teaching PeriodWinter
CoordinatorFani Petalidou
CommonNo
StatusActive
Course ID40000468

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

Registered students: 50
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specializationWinter-5.5

Class Information
Academic Year2019 – 2020
Class PeriodWinter
Faculty Instructors
Weekly Hours3
Class ID
600147617
Type of the Course
  • Scientific Area
Course Category
Knowledge Deepening / Consolidation
Mode of Delivery
  • Face to face
Digital Course Content
Language of Instruction
  • Greek (Instruction, Examination)
Prerequisites
Required Courses
  • 0303 Classical Differential Geometry I
  • 0203 Calculus III
  • 0204 Topology of Metric Spaces
  • 0205 Calculus IV
General Competences
  • Work autonomously
  • Work in teams
  • Work in an international context
  • Work in an interdisciplinary team
  • Generate new research ideas
Course Content (Syllabus)
Homeomorphic topological spaces. Topological manifolds. The notion of differentiable manifold, construction and examples of differentiable manifolds. Maps between manifolds. Submanifolds. Tangent vectors, tangent space and tangent vector bundle. Vector fields and Lie bracket. Covectors, cotangent space and cotangent bundle. Forms. The differential of a map, pushforward and pullback.
Keywords
Manifolds
Educational Material Types
  • Notes
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Communication with Students
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures1304.3
Reading Assigment321.1
Exams30.1
Total1655.5
Student Assessment
Description
Written examination
Student Assessment methods
  • Written Exam with Multiple Choice Questions (Summative)
  • Written Exam with Short Answer Questions (Formative, Summative)
  • Written Exam with Extended Answer Questions (Formative, Summative)
  • Written Assignment (Formative, Summative)
  • Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
- Διαφορίσιμες Πολλαπλότητες, B. Παπαντωνίου, Εκδόσεις Πανεπιστημίου Πατρών, 2013 - Διαφορικές Μορφές, Manfredo Do Carmo, Leader Books, 2010
Additional bibliography for study
1. Δημητρίου Κουτρουφιώτη, Διαφορική Γεωμετρία, Πανεπιστήμιο Ιωαννίνων 1994. 2. Loring W. Tu, An introduction to Manifolds, Universitext, Springer 2011. 3. John M. Lee, Introduction to Smooth Manifolds, GTM 218, Springer 2003. 4. M. Spivak, A comprehensive Introduction to Differential Geometry, Publish or Perish, Inc., 1999.
Last Update
15-03-2020