Electromagnetism, Fluids and Waves
Introduction
Waves
1. Introduction
2. Mathematical Preliminaries
3. Harmonic and Oscillatory Motion
4. Longitudinal Waves
5. Solutions to the Wave Equation
6. Transverse Waves
7. Dispersion Relations and Wave Energy
8. Polarisation of Waves
9. Standing Waves
10. Matter Waves
11. Doppler Shift
Electromagnetism
12. Introduction
13. Mathematical Preliminaries
14. Electrostatics
15. Solving Electrostatic Systems
16. Energy in an Electric Field
17. Magnetism
18. Magnetic Forces
19. Ampère’s Circuital Law
20. Faraday’s Law
21. Differential Forms and Maxwell’s Equations
22. Solutions to Maxwell’s Equations
23. Energy in an Electromagnetic field
24. Electromagnetic Scalar and Vector Potentials
Fluids
25. Introduction
26. Mathematical background
27. Visualising fluid motion
28. Divergence and vorticity
29. The velocity potential
30. Conservation law derivations
31. Shear stress and viscosity
32. Steady solutions
33. Bernoulli’s equation
34. Scaling arguments
35. Perturbations and asymptotics
36. Vortex transport
37. Unsteady: Water waves
38. Unsteady: Sound waves
39. Rotational reference frames
40. Geophysical phenomena
repository
open issue
Index
