MAT-61256 Geometric Analysis, 7 cr

Additional information

Moodle is used during the course
Suitable for postgraduate studies. The implementation will not be executed during the academic year 2016-2017.

Person responsible

Sirkka-Liisa Eriksson

Lessons

Implementation Period Person responsible Requirements
MAT-61256 2016-01 - Sirkka-Liisa Eriksson
The final exam or two partial exams

Learning Outcomes

After completion of the course the students knows the foundations of topological tools and differential calculus in Rn. The Student learn geometric algebras and their importance. The student is capable of applying them in geometric problems. The student knows the foundations of the analysis in higher dimensions using geometric algebras and the special case quaternions.

Content

Content Core content Complementary knowledge Specialist knowledge
1. Topological concepts and main results in R and in Rn. Continuous and differentiable functions.     
2. Inverse function theorom and implicit function theerem.  Primitive functions   
3. Introduction to geometric algebras, quaternions and their basic elements scalars, vectors, bivectors and multivectors     
4. Exterior product, contraction and geometric product and their geometric meaning. Calculation of vector derivatives and integrals using geometric algebras     

Instructions for students on how to achieve the learning outcomes

The grade of the course is based on the final exam or two partial exams. When the points for the final exam or the partial exams are 30% of the maximum, the grade of the course may be improved by bonus points collected from the instructed exercises and homework. The passing limit is 50% of the maximum. If the student is mastering the concepts, results, short proofs and examples type of problems the evaluation is 3. For the grade 4 the student should in addition to the previous level be able to independently apply theory more. For the grade 5 the student should independently deduce results, invent solutions and compare results more than in the previous levels.

Assessment scale:

Numerical evaluation scale (0-5)

Partial passing:

Completion parts must belong to the same implementation

Study material

Type Name Author ISBN URL Additional information Examination material
Summary of lectures   Geometric Analysis   Eriksson         Yes   
Summary of lectures             No   

Prerequisites

Course Mandatory/Advisable Description
MAT-60206 Mathematical Analysis Advisable    

Correspondence of content

There is no equivalence with any other courses

Updated by: Ikonen Suvi-Päivikki, 13.04.2016