Undergraduate Course: Differentiable Manifolds (MATH10088)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This course is an introduction to differentiable manifolds from an intrinsic point of view, leading to classical theorems such as the generalised Stokes¿ theorem. It extends the subject matter of Y3 Geometry from surfaces (embedded in R^3) to differentiable manifolds of arbitrary dimension (not necessarily embedded in another space). This provides the necessary concepts to start studying more advanced areas of geometry, topology, analysis and mathematical physics. |
| Course description |
- Definition of topological manifolds
- Smooth manifolds and smooth maps, partitions of unity
- Submanifolds and implicit function theorem
- Tangent spaces and vector fields from different points of view (derivations, velocities of curves)
- Flows and Lie derivatives
- Tensor fields and differential forms
- Orientation, integration and the generalised Stokes' Theorem
- Basic notions of Riemannian geometry
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Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
|
| Academic year 2015/16, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )
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| Assessment (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework 5%, Examination 95% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | Differentiable Manifolds | 2:00 | |
Learning Outcomes
- Explain the concept of a manifold and give examples.
- Perform coordinate-based calculations on manifolds.
- Describe vector fields from different points of view and indicate the links between them.
- Work effectively with tensor fields and differential forms on manifolds.
- State and use Stokes' theorem.
- Explain the concept of a Riemannian metric
|
Reading List
Recommended :
(*) John Lee, Introduction to smooth manifolds, Springer 2012
Michael Spivak, Calculus on manifolds, Benjamin, 1965
Theodor Bröcker & Klaus Jänich, Introduction to Differential Topology, CUP 1982
Frank Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer 1983
(*) Loring Tu, Introduction to Manifolds, Springer 2010
(*) are available to download from the University Library |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | DMan |
Contacts
| Course organiser | Dr Pieter Blue
Tel: (0131 6)50 5076
Email: |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: |
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