302737 (v.2) Physics 402

---

 

Area:	Department of Applied Physics
Credits:	25.0
Contact Hours:	4.0
Lecture:	2 x 2 Hours Weekly
Other Requisite(s):	Admission: to the physics honours program
Syllabus:	Contravariant and covariant tensors. The Einstein summation convention. Lorentz space. Symmetric and antisymmetric tensors. The gradient, divergence, curl and d Alembertian operators applied to tensors. The order of a tensor. The metric tensor. Rectilinear and curvilinear coordinates. The Einstein tensor. The line element for various coordinate systems. Converting from one coordinate system to a different coordinate system. Cartesian to spherical. In the last six weeks, you will know the definition and application of - flat space and Riemannian space. Christoffel symbols or connection coefficients. The curvature tensor. The Ricci tensor. The principle of equivalence and its implications. General relativity and coordinate geometry problems - calculate the angle of the deflection of light as it passes the sun. Do this calculation classically and compare with the general relativity result. Given a specific line element determine if the space is curved. Determine the line elements of several geometrical shapes. Calculate the connection coefficients for several geometrical shapes.
Unit Outcomes:	On successful completion of this unit the student will gain an introduction to tensors and how they can be used to transform from one co-ordinate system to another, and their applications to General Relativity. The student will become equipped with the necessary knowledge of tensors so that they can solve coordinate geometry problems and some of the more interesting problems that General Relativity poses.
Text and references listed above are for your information only and current as of September 30, 2003. Please check with the unit coordinator for up-to-date information.
Unit References:	No prescribed references.
Unit Texts:	Spiegel, M. R., 1974, 'Schaums Outline of Theory and Problems of Vector Analysis: and an Introduction to Tensor Analysis' McGraw-Hill, New York. Yilmaz, H., 1965, 'Introduction to the Theory of Relativity and the Principles of Modern Physics', McGraw Hill, New York. Peebles, P. J., 1993, 'Principles of Physical Cosmology', Princeton University press.
Unit Assessment Breakdown:	4 x Assignments 70%. Final Examination 30%.
Year Location Period Internal Area External Central External 2004 Bentley Campus Semester 2 Y