Office:
3.4
Hamilton Building
Office Hours: email for appointment
Phone: 01 896 4027
Email: frolovs@maths.tcd.ie
Tutors / Graders
Philipp Hähnel, haehnel@maths.tcd.ie
Recommended Reading
Geometrical Methods of Mathematical Physics, B. Schutz, (Cambridge University Press 1980);
Differential Geometry of Manifolds, S. Lovett, (AK Peters, Ltd. 2010)
Applied Differential Geometry, W.L. Burke, (Cambridge University Press 1985)
Lecture Notes on GR, Sean M. Carroll. Available here
Advanced General Relativity,Sergei Winitzki. Available here
Class Meetings
Tutorials:  Wednesday 
15:0015:50 
Synge,
Hamilton Building 
Synge 
Lectures: 
Wednesday 
11:0012:50 
Salmon Theatre, Hamilton Building 
Sal1 

Thursday 
9:009:50 
LLoyd Building 
LB01 
There will be tutorials every week starting
with 11 October 2016.
Learning Outcomes
On successful completion of this module, students will be able to:
Obtain a coordinateinduced basis for the tangent space and cotangent space at points of a differentiable manifold, construct a coordinate induced basis for arbitrary tensors and obtain the components of tensors in this basis;
Determine whether a particular map is a tensor by either checking multilinearity or by showing that the components transform according to the tensor transformation law;
Construct manifestly chartfree definitions of the Lie derivative of a function and a vector, to compute these derivatives in a particular chart and hence compute the Lie derivative of an arbitrary tensor;
Compute, explicitly, the covariant derivative of an arbitrary tensor;
Define parallel transport, derive the geodesic equation and solve problems invloving parallel transport of tensors;
Obtain an expression for the Riemann curvature tensor in an arbitrary basis for a manifold with vanishing torsion, provide a geometric interpretation of what this tensor measures, derive various symmetries and results involving the curvature tensor;
Define the metric, the LeviCivita connection and the metric curvature tensor and compute the components of each of these tensors given a particular lineelement;
Define tensor densities, construct chartinvariant volume and surface elements for curved Lorentzian manifolds and hence construct welldefined covariant volume and surface integrals for such manifolds;
Two hour End of year Final examination.

0% 

100% 
These
questions are here and
the file should be checked regularly for updates.
The file is here, and it should be checked regularly for updates.
Sample Final Exam Questions
The
file is here, and it might be updated.
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You are welcome to submit any comments you have about this class here.