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 many of the following topics: 
 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

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
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 )

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
On completion of this course, the student will be able to:
 Explain the concept of a manifold and give examples.
 Perform coordinatebased 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: P.Blue@ed.ac.uk 
Course secretary  Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk 

