Special Topics in Geometry (MAE822): Διαφορά μεταξύ των αναθεωρήσεων

Από Wiki Τμήματος Μαθηματικών
Χωρίς σύνοψη επεξεργασίας
Χωρίς σύνοψη επεξεργασίας
Γραμμή 1: Γραμμή 1:
* [[Ειδικά Θέματα Γεωμετρίας (ΜΑE822)|Ελληνική Έκδοση]]
* [[Ειδικά Θέματα Γεωμετρίας (ΜΑE822)|Ελληνική Έκδοση]]
* [[Undergraduate Courses Outlines]]
{{Course-UnderGraduate-Top-EN}}
* [https://math.uoi.gr/index.php/en/ Department of Mathematics]


=== General ===
=== General ===

Αναθεώρηση της 09:44, 26 Νοεμβρίου 2022

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAE822

Semester

8

Course Title

Special Topics in Geometry

Independent Teaching Activities

Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6)

Course Type

Special Background

Prerequisite Courses -
Language of Instruction and Examinations

Greek, English

Is the Course Offered to Erasmus Students

Yes

Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

This course introduces the notion of differential forms. The aim of the course is to prove Stokes theorem for manifolds with boundary and to provide applications in differential geometry as well as in other areas of mathematics. The course requires tools from linear algebra, calculus of several variables, topology and elementary differential geometry. On completion of the course the student should be familiar with differential forms and the meaning of Stokes theorem.

General Competences
  • Working independently
  • Decision-making
  • Production of free, creative and inductive thinking
  • Criticism and self-criticism

Syllabus

Differential forms in Euclidean space, line integrals, differentiable manifolds (with or without boundary), integration of differential forms on manifolds, theorem of Stokes and applications, Poincare lemma, differential geometry of surfaces, structure equations.

Teaching and Learning Methods - Evaluation

Delivery

Classroom (face-to-face)

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures (13X3) 39
Working independently 78
Exercises-Homeworks 33
Course total 150
Student Performance Evaluation

Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems.

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

  • M. do Carmo, Διαφορικές Μορφές, Θεωρία και Εφαρμογές, Prentice-Hall, Πανεπιστημιακές Εκδόσεις Κρήτης, 2010.