Title  ΔΙΑΦΟΡΙΣΙΜΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΙΙ / Differential Manifolds II 
Code  0333 
Faculty  Sciences 
School  Mathematics 
Cycle / Level  1st / Undergraduate 
Teaching Period  Spring 
Coordinator  Fani Petalidou 
Common  No 
Status  Active 
Course ID  40000471 
Programme of Study: UPS of School of Mathematics (2014today)
Registered students: 0
Orientation  Attendance Type  Semester  Year  ECTS 

Core  Elective Courses belonging to the selected specialization  8  4  5.5 
Academic Year  2019 – 2020 
Class Period  Spring 
Faculty Instructors 

Weekly Hours  3 
Class ID  600147686

Type of the Course
 Scientific Area
Course Category
Knowledge Deepening / Consolidation
Mode of Delivery
 Face to face
Digital Course Content
 eStudy Guide https://qa.auth.gr/en/class/1/600147686
Language of Instruction
 Greek (Instruction, Examination)
 English (Instruction, Examination)
 French (Instruction, Examination)
Prerequisites
Required Courses
 0131 Group Theory
 0303 Classical Differential Geometry I
 0304 Differential Manifolds I
 0201 Calculus I
 0202 Calculus II
 0203 Calculus III
 0205 Calculus IV
 0206 Differential Equations
 0233 General Topology
 0235 Partial Differential Equations
 0108 Linear Algebra
Learning Outcomes
Acquisition and deepening in the basic concepts of the theory of smooth manifolds and on introductory concepts of Riemannian geometry.
General Competences
 Apply knowledge in practice
 Work autonomously
 Work in teams
Course Content (Syllabus)
Elements from the theory of smooth manifolds. Riemannian manifolds. Linear connections. Geodesics and curvature. Sectional curvature. Jacobi fields and second fundamental form.
Educational Material Types
 Notes
 Book
Course Organization
Activities  Workload  ECTS  Individual  Teamwork  Erasmus 

Lectures  130  4.3  ✓  
Seminars  
Reading Assigment  32  1.1  
Exams  3  0.1  
Total  165  5.5 
Student Assessment
Description
Presentation, Written Examination
Student Assessment methods
 Oral Exams (Formative)
Bibliography
Additional bibliography for study
1. John M. Lee, Riemannian manifolds. An introduction to curvature, GTM 176, SpringerVerlag 1997.
2. Loring W. Tu, An introduction to Manifolds, Universitext, Springer 2011.
Last Update
14052019