Differential Manifolds I

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: 29
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specialization745.5

Class Information
Academic Year2018 – 2019
Class PeriodWinter
Faculty Instructors
Weekly Hours3
Class ID
600121405
Type of the Course
  • Scientific Area
Course Category
Specific Foundation / Core
Mode of Delivery
  • Face to face
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
  • English (Examination)
  • French (Examination)
  • German (Examination)
Prerequisites
Required Courses
  • 0303 Classical Differential Geometry I
  • 0201 Calculus I
  • 0202 Calculus II
  • 0203 Calculus III
  • 0204 Topology of Metric Spaces
  • 0205 Calculus IV
  • 0108 Linear Algebra
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. Differentiable manifolds. The tangent space. Differential of a map. Tensor algebra. Tensor fields. Gradient and covariant diffrentiation of functions. Lie brackets. Covariant differentiation of tensor fileds. Affine connections. Parallel transport of tangent vectors. Geodesics. Parallel vector fields. The curvature tensor.
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 Short Answer Questions (Formative, Summative)
  • Written Assignment (Formative, Summative)
  • Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Β. Παπαντωνίου: Διαφορίσιμες Πολλαπλότητες
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
14-05-2019