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 
The course will include the following topics:
 Smooth manifolds, the manifold topology and submanifolds as level sets.
 Tangent and cotangent spaces, derivative of a smooth map.
 Tangent bundle, vector fields, derivations, flows, Lie derivative.
 Vector bundles, tensor fields.
 Differential forms, Cartan calculus, de Rham complex.
 Orientation, integration, Stokes's theorem.

Information for Visiting Students
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
Learning Outcomes
On completion of this course, the student will be able to:
 Explain the concept of a manifold and give examples.
 Perform coordinatebased and coordinatefree 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.

Reading List
Recommended in addition to materials provided:
(*) John Lee, Introduction to smooth manifolds, Springer 2012
Michael Spivak, Calculus on manifolds, Benjamin, 1965
Theodor Broecker & Klaus Jaenich, Introduction to Differential Topology, CUP 1982
(*) 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  Prof JosÃ© FigueroaO'Farrill
Tel: (0131 6)50 5066
Email: 
Course secretary  Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: 

