Special Topics in Geometry (MAE822)

Undergraduate Courses Outlines - Department of Mathematics

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)	-

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

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