Embedded Files
ANNOUNCEMENT :
ANNOUNCEMENT :
Lecture Videos Available Under Talking Slides Heading Below
Lecture Videos Available Under Talking Slides Heading Below
Course Code MATZ6844
Course Code MATZ6844
UFS 16 Credits
UFS 16 Credits
Overview
Overview
The study of Manifolds and Tensor permits a coordinate invariant description of physical and mathematical phenomenon. A number of powerful techniques for describing the properties of an object, in a manner that is not dependent of the coordinate chart chosen, are develop. How Tensors transform between coordinates systems are also explored. Tensor techniques are extensively used in Fluid Dynamics, the study of Elasticity, Crystallography, Computer Graphics, General Relativity and other fields of physics, computer science and economics.
Concepts such as the vectors, one forms, the metric, signature, covariant differentiation, geodesics, parallel transport and curvature are introduced with examples from a variety of fields.
The last few lectures will focus on examples from General Relativity and the study of Black Holes.
Prerequisites
Prerequisites
Knowledge of solving ordinary differential equations on the level of A first Course in Differential Equations - Dennis G Zill.
Vector Calculus
Lecturer
Lecturer
Jeandrew Brink, Contact: BrinkJ2@ufs.ac.za , WWG 109
Course Material
Course Material
Notes, articles assignments posted on this webpage.
**A Short Course in General Relativity - Foster and Nighting 3rd Ed Springer (F&N)
**Introduction to General Relativity, Black Holes, and Cosmology - Yvonne Choquet-Bruhat (CB)
**A Relativist's Toolkit : The Mathematics of Black-Hole Mechanics by Eric Poisson
Tensor Calculus, JL Synge and A Schild Canada 1949
**General Relativity, R Wald, 1984 isbn 0-226-87033-2 (Chap 2 and 3)
The Mathematical Theory of Black Holes. S Chandrasekhar 2005
**(Copy in UFS Library)
Lectures and Consultation Hours
Lectures and Consultation Hours
Lecture 1:
Wednesday 10:10-11.00 WWG 119
Thursday 9:10-10 WWG 119
Consultation:Wed 11.10 am -12am WWG 109
Slides
Intro Lectures Curves Surfaces Origami
Lec1 , Lec2, Lec3, Lec4, Lec5,Lec6
Lec7, Lec8, Lec9, Lec10, Lec11, Lec12
Lecture notes on Schwarszchild Solution for Lecture 12. Pages 9-17 were covered in Lecture. Pages 18-22 cover the null geodesics also interesting ... don't worry about Carlsons integrals too much. But look at the picture 5 which gives the light cones.
Consultation hours
Consultation hours
Tue 11:00-12:00
Wed 14:00-15:00
Thurs 12:00-13:00
Evaluation
Evaluation
Semester Mark is constituted out of 5 assignments each counting 20% of the semester mark.
A semester mark of 45% or more must be attained to gain admission to the exam. An exam mark of at least 40 % must be attained to pass the course.
In the final mark, the semester mark is weighted 60% and exam result 40%. A final mark of at least 50 % must be attained to pass the course.
Videos and other Links
Videos and other Links
Cosmos - Carl Sagan - 4th Dimension
Talking Slides
Talking Slides
2023
2023
Extra Background
Extra Background
Derivation of the Euler Lagrange Equations Calculus of Variations
Lectures on Manifolds (Wald)
Lectures on Manifolds (Wald)
Lecture 21 Video Manifolds 12 A Manifolds 12 B
Lecture 18 Video Manifolds 9 Parallel Transport and Derivatives
Lecture 13 Intro To Pulsar J0737
Lecture 9 Video Intro to Manifolds Definitions Vectors Charts
Origami Lectures
Origami Lectures
Lecture Notes Slides 2 Origami Curved Folds
Lecture 8 Video Dynamics of a circular crease fold
Lecture 7 Video Curvature conditions Curved Folds
Lecture 6 Video Principle Curvature Directions, Application Origami
Lecture 5 Vid Metric and Curvature of Parametric Surfaces in 3D
Lecture notes: Intro Curved Surfaces in 3D
Lecture 3 Ruled and developable Surfaces
Intro Lecture Notes Curves Surfaces
Lecture 2 Curves in 3 D, Surfaces Intro
2021
2021
Lecture 11: Geodesic Deviation Video
Problem Sets 2023
Problem Sets 2023
Tutorial 5 Due Thurs 26 Oct in Class
Tutorial 3 Due 14 Sept
Tutorial 2 Due 5 Sept
Problem Set 1: Due strictly before 15 August
Past Activities:
Past Activities:
Students analyse MeerKAT data from a pair of neutron stars in a tight 2-hour orbit and verify that it exhibits space-time curvature, eclipses, and its orbit is decaying by a few cm per day due to the emission of gravitational waves.
Grading Policy
Grading Policy
No tutorials will be accepted after the due date. Hard copies must be handed in for grading. No scanned or emailed homework copies will be accepted.
In the unfortunate circumstance of missing a semester test, the lecturer must be notified within 24 h. In the case of illness, a doctors certificate must be provided. A make up / special test, may be oral and/or written and will cover all the semesters work.
Great emphasis is placed on original, creative work. A well argued, understood, possibly numerically ''wrong'' answer is of much better value than one copied from the web. Collaboration on homework sets is allowed provided collaborators are given credit, and the person handing in the answer can defend the reasoning. If other sources are used, such as, books, articles etc they must be referenced. Should plagiarism be suspected, a student will be asked to solve a similar problem on the blackboard during a consultation session, to obtain the marks for the tutorial.
Page updated
Google Sites
Report abuse