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Course Catalog 2013-2014
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 |
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Requirements
The final exam or two partial exams
Completion parts must belong to the same implementation
Principles and baselines related to teaching and learning
During the course there are instructed exercises that helps learning. Moodle study platform is used during the course and extra material may be handed out through that there and students may discuss about there problem.-
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:
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 |
| 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. |