Course Materials 

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Exam Review

• Exam I: Review, Sample Exam (answers)
• Exam II: Review, Sample Exam
• Final Exam: Sample Final Exam
• Dark Matter https://www.youtube.com/watch?v=NdaQWj5ykso
• Inflationary Cosmology https://www.youtube.com/watch?v=ANCN7vr9FVk
• The universe before the big bang https://www.youtube.com/watch?v=hszc-VjU1_E&t=358s
• Universe or Multiverse? https://www.youtube.com/watch?v=qlHvQLxb4cw
• Cosmology: the physical edges of the Universe https://www.youtube.com/watch?v=-xhb90JSHnA

Handouts

• Minkowski Diagrams Paper
• Maple Output for Train Problem PDF
• Euler Equations and Geodesics
• Derivation of Geodesic Equation
• Wormhole Geodesic Computation and Handout

Introduction - past talks

• "Listening for Einstein's Ripples in the Fabric of the Universe" (2016)
• "Is Time Real or an Illusion? The Physics of Time" (2017)
• "Window to the Dark Side of the Universe" (2012)
• "The First Three Minutes of the Universe" (2008)

Geometry

• History of Non-Euclidean Geometry

• The Geometry of the Sphere

• Spherical Geometry Demo

• Lunes and Triangles

• Spherical Easel

• Flatland - A Romance of Many Dimensions

  • Sequels ...

• Geometry of Black Holes

Principle of Relativity

• Biography of Galileo
• Galileo's Parable of the Ship
• Three Levels of Understanding Physical Relativity
• The Principle of Least Action
• Quantum Physics Explains Newton's Laws of Motion
• Transformations
  • Rotation
  • Galilean Transformation Axes
  • Lorentz Transformation Axes

Special Relativity

• Dr. Herman's Notes
  • Minkowski Diagrams Paper
  • Figures from paper
    • Boost Axes,
    • Simultaneous Events in S
    • Time Dilation, fixed in S
    • Length Contraction, fixed in S
    • Time Dilation, fixed in S'
    • Length Contraction, fixed in S'
  • Train Problem - Plot, Maple File, Maple PDF, Answer
  • Boost Grids, Pics: beta = #/c - 1, 2, 3, 4, 5, 6, 7, 8, 9
• Brehme's Paper, Spactime Diagram Software
• Relativity Notes -
• Relativity Lecture Notes - with problems
• Einstein Light
• Think Like Einstein
• How Did Einstein Discover Relativity?
• Dummies guide to Special Relativity
• Introduction to Relativity
• "On the Electrodynamics of Moving Bodies"

Geometry

• History of Non-Euclidean Geometry

• The Geometry of the Sphere

• Flatland - A Romance of Many Dimensions

  • Sequels ...

Four Vectors and Lagrangians

• The four-dimensional space-time
• Four Vectors - at HyperPhysics or Wikipedia
• Summation Convention
• Lagrangian Formulation
• Basic Lagrangian Mechanics
• The Geodesic Equation
• Derivation of Geodesic Equation - Derivation
• Geodesics on a Sphere
• Christoffel Symbol Computation in Maple Christoffel.mws
• Wormhole Geodesic Computation and Handout
• Other Packages:
  • Sage Math
  • Maxima - Example, and ctensor example
  • Christoffel Symbols and Geodesic Equation - Mathematica
• Geodesicviewer - Stuff projects are made of!

Schwarzschild Spacetime

• Schwarzschild Metric
• Maple Worksheets Schwarz.mws, Precession.mws (PDF Version)
• Chapter 9 Lecture: The Schwarzschild Spacetime
• Maple - Eddington-Finkelstein
• Geodesic Problem
• Penrose Diagrams
• Kerr-Newman Metric Review

Embedding Spacetimes

• Visualising spacetimes via embedding diagrams - Talk, Paper by A. Cipko, S. Hledík and Z. Stuchlík,
• Spacetime Embedding Diagrams for Black Holes - Marloff
• Visualizing curved spacetime - Jonssona

Observations

• Sloan Sky Digital Survey
• The 2df Galaxy Redshift Survey

Cosmic Metric

• Friedmann-Lemaitre-Robertson-Walker Metric
• Summary of Formulae for RW Metric
• Distance Measures in Cosmology
• Misconceptions about expansion

Friedmann Equation

• Wikipedia
• Newtonian derivation
• Susskind's Cosmology Lecture #8
• Solutions of the Friedmann Equation and also Here with applet
• The density parameter
• The Cosmic Triangle
• The Cosmic Triangle Paper

Big Bang Cosmology

• Big Bang Timeline Images
• NASA Intro to Cosmology
• BB Timeline - PDF
• Blackboards Timeline of the Universe (Left Half, Right Half, Most Recent)
• Monopole Problem - Unification of forces diagram

Einstein Field Equation

• The Meaning of Einstein's Equation
• Einstein's Equation -  PPT
• The Einstein Field Equation - NCSA
• Einstein Field Equations for Beginners - YouTube Video
• Leonard Susskind's Lectures
  • Lecture 3 (40 min in) discussion of tensors
  • Lecture 4 Differentiation
  • Lecture 5 Covariant Derivatives
  • Lecture 7 Curvature

Alternative Theories

• MOND - Modified Newtonian Dynamics
• MOND - Recent Results
• MOND Pages
• Lambda CDM vs MOND
• Non-standard cosmology

Miscellaneous

• Kip Thorne - Einstein's General Relativity
• Virtual Trip to a Black Hole
• "-- All You Zombies --", Time PPT - See the movie Predestination

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