Course Catalog 2014-2015
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Basic Pori International Postgraduate Open University

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Course Catalog 2014-2015

MAT-61256 Geometric Analysis, 7 cr

Additional information

Moodle is used during the course
Suitable for postgraduate studies

Person responsible

Sirkka-Liisa Eriksson

Lessons

Study type P1 P2 P3 P4 Summer Implementations Lecture times and places
Lectures
Excercises


 


 
 4 h/week
 3 h/week
+3 h/week
+3 h/week


 
MAT-61256 2014-01 Monday 10 - 12 , TB223
Tuesday 10 - 12 , TB223
Tuesday 10 - 12 , TD308
Monday 10 - 15 , TD308

Requirements

The final exam or two partial exams
Completion parts must belong to the same implementation

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 (1-5) will be used on the course

Partial passing:

Completion parts must belong to the same implementation

Study material

Type Name Author ISBN URL Edition, availability, ... Examination material Language
Summary of lectures   Geometric Analysis   Eriksson         Yes    English  
Summary of lectures             No    English  

Prerequisites

Course Mandatory/Advisable Description
MAT-60206 Mathematical Analysis Advisable    

Prerequisite relations (Requires logging in to POP)

Correspondence of content

There is no equivalence with any other courses

More precise information per implementation

Implementation Description Methods of instruction Implementation
MAT-61256 2014-01 We present geometric methods in analysis in R^n. The course is useful for those who want to become a math teacher. It is also usefull for students who want have deeper understanding of analysis in higher dimensions.        

Last modified12.02.2014