Fourier (Harmonic) series
- The basics (from "ask a mathematician")
- The mathematics (from Lamar University)
- The fundamental equations with sine as the first term - a Fourier series; computing harmonic coefficients; computing signal power; computing explained variance
- The fundamental equations with cosine as the first term. (This version is slightly more common in the literature.)
- Wait! What? The beauty of a bizarre notion. (Note: the term "imaginary number" originated in the 17th century as a derogatory term, see Wiki)
- Intuitive understanding of Euler's formula
- The fundamental equations for complex Fourier series
- Examples of converting between complex Fourier series and real version of Fourier series. Courtesy Nathan Pflueger of Amherst University
- Supplementary material on complex Fourier series. Courtesy Swarthmore College.
- Animation, example of drum normal modes
- Normal modes and using them for wave solutions
- Linearization of equations by perturbation method
- Dispersion relationship, phase speed, and group velocity
- 1) Animation of phase speed and group velocity 2) Another animation 3) Animation of dispersive vs nondispersive waves 4) General video on wave dispersion
- Video lecture on wave dispersion. Courtesy Dr. Hillary Weller. Accompanying notes to video.
- Video of boat wake dispersion.
- Basic discussion of wave types in the atmosphere
- Summary figure on atmospheric wave types
- Characteristics of atmospheric wave types
- General (intermediate) water waves, shallow water waves, and deepwater waves. Which one is NOT dispersive? Video on ocean wave dispersion
- Rossby waves. Their westward propagation mechanism relates to how vorticity is redistributed. Graphic showing mechanism.
- Sound waves. Aside --- converting thermodynamic equation to its natural log version
- Waves on a discontinuity (like ocean waves)
