Applied Tensor Analysis (MAE543)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	ΜΑΕ543
Semester	5
Course Title	Applied Tensor Analysis
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The course is an introduction to the concepts of Tensor Analysis. The objectives of the course are: Development of the theoretical background in matters relating to Tensor Analysis. Ability of the student to apply the basic concepts of Tensor Analysis. Upon completion of this course the student will be able to solve with analytical methods simple problems of Tensor Analysis and deepen further understanding of such methods.

General Competences

The course aims to enable the undergraduate students to develop basic knowledge of Applied Tensor Analysis and in general of Applied Mathematics. The student will be able to cope with problems of Applied Mathematics giving the opportunity to work in an international multidisciplinary environment.

Syllabus

The tensor concept, Invariance of tensor equations, Curvilinear coordinates, Tensors in generalized curvilinear coordinates, Gauss, Green and Stokes theorems, Scalar and vector fields, Nabla operator and differential operators, Covariant differentiation, Integral theorems, Applications to Fluid Dynamics.

Teaching and Learning Methods - Evaluation

Delivery	In class
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures 39 Study of theory 78 Home exercises 33 Course total 150
Student Performance Evaluation	Weekly assignments Final project Written examination at the end of the semester

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. Additionally:

• A. I. Borisenko and I. E. Taparov, Vector and Tensor Analysis, Edition: 2/2017, Editor: G. C. FOYNTAS (in Greek).
• H. Lass, Vector and Tensor Analysis, Edition: 2/2017, Editor: G. C. FOYNTAS (in Greek).