## Topic outline

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• This is the material from the online course LIGO: Waves and Gravity. It was offered for credit through Sonoma State University in the summer of 2015, before the discovery of gravitational waves.

• 1

This unit reviews the differential form of Maxwell's Equations and demonstrates that accelerating charges produce electromagnetic waves in a dipole configuration.

The text and 7 homework problems are included within the PDF file linked below. There is an additional handout to review vector operators.

• This PDF file has the text and 7 homework problems.

• This background handout defines the standard vector operators used in Maxwell's Equations, the wave equation and other similar physics problems. It  includes definitions in Cartesian coordinates for the divergence, gradient, curl,  and Laplacian, as well as the vector and scalar triple products.

• 2

### Geometry and Gravity for Weak Fields

This unit begins by extending Special Relativity concepts into accelerating frames, and connecting it to Maxwell's Equations. Then a slightly more mathematical treatment of curvature is presented, leading up to the Einstein Field Equations. Applications of the Field Equations to weak fields and predictions for gravitational waves conclude the unit.

The text and 10 homework problems are included within the PDF file below. Also included is a background supplement with additional mathematical background.

• This PDF file has the text and 10 homework problems.

• This background handout includes many of the derivations underlying the text for Geometry and Gravity for Weak Fields. It also includes additional information about hyperbolic functions, and matrix operations.

• 3

### Astrophysical Sources of Gravitational Waves

This unit summarizes the physics and expected signals from the three most likely sources of gravitational waves: coalescing binary systems, impulsive events (such as supernovae or gamma-ray bursts) and continuous wave sources (such as spherically asymmetric pulsars). We also touch on stochastic sources of gravitational radiation, and briefly discuss other observatories that are planned for future observations of different bands in the gravitational wave spectrum.

This section also includes some links to publicly accessible interactive activities that you are free to use and share. For direct links to the materials in this unit, and many more, see the Additional Resources sections below.

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This section includes links and short descriptions of some valuable resources on Special Relativity, as well as copies of some copyrighted journal articles that have been downloaded for educational uses, in accordance with fair use policies.

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This section includes links and short descriptions of some valuable resources on General Relativity, as well as copies of some copyrighted journal articles that have been downloaded for educational uses, in accordance with fair use policies.

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This section includes links and short descriptions of some valuable resources on black holes.

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• Courses

• LIGO

• Waves and Gravity

• Participants