MA2505 Tensors and Riemannian geometry

Single subject course, 7.5 ECTS credits, Second cycle, spring semester 2012
This course occasion will not start spring semester 2012!

Overview

During this course students will obtain basic knowledge on tensor calculus and Riemannian geometry. In particular, they will learn how to use them in classical and relativistic mechanics. They also learn to use them for tackling linear partial differential equations with variable coefficients.

Application date

2011-October-15

Course period

2012-January-16 until
2012-March-25

Mode of delivery

On campus (face-to-face), Day-time, part time 50 %

Teaching location

Karlskrona

Language of instruction

English

Syllabus in English

Coming soon

Main field of study

Mathematics

Admission

Prerequisites

Transformation Groups and Lie Algebras MA2411, 7.5 credit points.

Application date

2011-October-15

Course period

2012-January-16 until
2012-March-25

Mode of delivery

On campus (face-to-face), Day-time, part time 50 %

Teaching location

Karlskrona

Language of instruction

English

Syllabus in English

Coming soon

Main field of study

Mathematics

Learning Outcomes

Content

Tensor calculus. Covariant and contravariant tensors. Definition of a Riemannian space. Covariant differentiation of tensors. The curvature tensor. Geodesics. Isometric motions. Conformal Riemannian spaces and conformal transformation groups. Riemannian spaces associated with linear second-order partial differential equations. The covariant Laplace and wave equations, their symmetry groups. Discussion of the Huygens
principle. Elements of special and general relativity.

Learning outcomes

On completion of the course the student will be able to:
• obtain competence in the field of Riemannian geometry
• develop analytic skills and working knowledge in presenting results using tensors
• know the terminology and use the literature.

Generic Skills

The following generic skills are trained in the course:

• ability to analysis and synthesis

• ability to read the literature in English

• ability to present results in the written form.

Course literature and other teaching material

Ibragimov, N.H. (2008). Tensors and Riemannian geometry with applications to differential equations and relativity. ALGA Publications, Karlskrona, Sweden.

Application date

2011-October-15

Course period

2012-January-16 until
2012-March-25

Mode of delivery

On campus (face-to-face), Day-time, part time 50 %

Teaching location

Karlskrona

Language of instruction

English

Syllabus in English

Coming soon

Main field of study

Mathematics

Stucture - Literature

Course literature and other teaching material

Ibragimov, N.H. (2008). Tensors and Riemannian geometry with applications to differential equations and relativity. ALGA Publications, Karlskrona, Sweden.

Learning methods

Teaching is conducted through lectures and exercises. During the course students solve recommended exercises on their own and then discuss together in the class. The final assignment, however, is solved and written by each student individually.

Work placement

No work placement is included in the planned learning activities. BTH is aiming for a close contact with the surrounding community when developing courses and programmes.

Teachers

Examiner
Raisa Khamitova

Course Manager
Raisa Khamitova

Planned learning activities

Time allocation

On average, a student should study 200 hours to reach the learning outcomes. This time includes all the various available learning activities (lectures, self studies, examinations, etc.). This estimation is based on the fact that one academic year counts as 60 ECTS credits, corresponding to an average student workload of 1 600 hours. This may vary individually.

Application date

2011-October-15

Course period

2012-January-16 until
2012-March-25

Mode of delivery

On campus (face-to-face), Day-time, part time 50 %

Teaching location

Karlskrona

Language of instruction

English

Syllabus in English

Coming soon

Main field of study

Mathematics

Examination

Assessments

Component examinations for the course
Code Title ECTS credits Grade
1105 Project 7.5 F/P/3/4/5

Grading

The course will be graded Fail, Pass, 3, 4 or 5 .

On request grades according to ECTS will be given.

Future exams

No upcoming, centrally coordinated, examinations for this course were found.

To participate in a centrally coordinated examination, you must enroll in Student's Portal, no later than fifteen days before the examination.

Time and location for the examination will be published about 5 days in advance.

There might be other scheduled examinations. Information concerning these examinations are available in It's Learning or at other places that the person who is responsible of the course will refer to.

Course Evaluation

The course manager is responsible for the views of students on the course being systematically and regularly gathered and that the results of the evaluations in various forms affect the form and development of the course.

Application date

2011-October-15

Course period

2012-January-16 until
2012-March-25

Mode of delivery

On campus (face-to-face), Day-time, part time 50 %

Teaching location

Karlskrona

Language of instruction

English

Syllabus in English

Coming soon

Main field of study

Mathematics

 

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