# Differential Manifolds

 Title ΔΙΑΦΟΡΙΣΙΜΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ / Differential Manifolds Code 0304Α Faculty Sciences School Mathematics Cycle / Level 1st / Undergraduate Teaching Period Winter Common No Status Active Course ID 600019939

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

Registered students: 71
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specializationWinter-5.5

 Academic Year 2022 – 2023 Class Period Winter Faculty Instructors Fani Petalidou 39hrs Weekly Hours 3 Class ID 600211757
Course Type 2011-2015
Knowledge Deepening / Consolidation
Mode of Delivery
• Face to face
• Distance learning
Digital Course Content
Prerequisites
Required Courses
• 0201 Calculus I
• 0233 General Topology
• 0110 ELEMENTS OF LINEAR ALGEBRA
• 0305 ELEMENTS OF ANALYTIC GEOMETRY
• 0306 INTRODUCTION TO GEOMETRY I
• 0108Α Linear Algebra
• 0202Α Calculus II
• 0203Α Calculus III
• 0204Α Topology of Metric Spaces
• 0205Α Calculus IV
• 0206Α Differential Equations
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 Course Teaching
• Use of ICT in Communication with Students
• Use of ICT in Student Assessment
Course Organization
Lectures1103.7
Written assigments
Exams30.1
Total1655.5
Student Assessment
Description
Home work - Γραπτή Εργασία
Student Assessment methods
• Written Exam with Extended Answer Questions (Formative, Summative)
• Written Assignment (Formative, Summative)
• Oral Exams (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 - Γεωμετρία Πολλαπλοτήτων, Πολλαπλότητες Riemann και Ομάδες Lie, http://hdl.handle.net/11419/146