Course Materials 

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The main text for this course is a book written by Dr. Herman: An Introduction to Fourier Analysis. Pages with color and some Errata.

We will also use resources from the web. These links are being updated for Spring 2026.

• Gauss and the FFT

• The Vibrating String Controversy

  • Unpublished resolution

• The Fourier Transforms and its Applications - Stanford U, YouTube
• See Fourier Series and Gibbs Phenomena by Donny Lee
• Mobius Transformations Revealed - complex analysis
• A Crash Course in Contour Integration - complex analysis
• Fourier Transform Film, I will derive
• Last Class Example: PDF
  • Files SigAnal.mlx, firstbird.wav, LIGO Data NumL.txt, NumH.txt

Reviews for Exams

• Review #1, Sample Exam

• Review #2, Sample Exam

• Review #3, Sample Exam

• Final Review, Sample Final

• Project Files

Sequences and Infinite Series

• Sequences and Series in Maple

• Overview of sequences and series - See additional material, problems and videos

• SOSMath - Sequences, Series, Geometric Series, Power Series, 

• Hyperbolic functions

• How Small is Small? - Talk by Dr. Herman

• De Moivre's 1707 paper and 1722 paper with translation
  compared to Euler's proof (1749, E170, E170en.pdf, p. 43) at Euler Archive
  A list of translations
• Traite du triangle arithmetique ... Pascal (1665) and a translation
• Origin of Taylor Series (12:18)
• The Story of the Binomial Theorem J. L. Coolidge
• Dr. Herman's List of Calculus Books and other references

Fourier Series

• Fourier Series and Waves

• SOS Math - Fourier Series

• Fourier Series and Convergence

• Fourier Series - Eric Weinstein's World of Math

• Computer Computation

  • Maple Worksheets - fseries.mws, PlotFS.mws, EvenOdd.mws

  • MATLAB plotfs.m (symbolic), plotfs0.m (not symbolic), FScoeff.m

    • GNU Octave - MATLAB clone

  • Desmos Fourier Series Examples 1 and 2

  • Wolframalpha.com - Fourier series examples

    • sum_(k=1)^10(4/pi sin((2 k-1)*x)/(2 k-1))

    • sum_(k=1)^10(4/pi sin((2 k-1)*x)/(2 k-1))

    • sum_(n=1)^10(cos(2 n pi x)/(n pi)^2- sin(2 n pi x)/(n pi))

  • SageMath, Example:  http://sage.brandoncurtis.com/fourier.html

  • Python fsplot.py or fsplot.txt

    • MIT Binder or Try Jupyter
    • https://www.educative.io/answers/how-to-implement-fourier-series-in-python

  • Software for Computing

• The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet ...- Google Books Result

• Note on Gibbs Phenomenon, 1925

• The Overshoot (12:28)

• Historical Notes on the Gibbs Phenomenon
• The Gibbs-Wilbraham Phenomenon: An Episode in Fourier Analysis - E. Hewitt, R. E. Hewitt, 1979
• Henry Wilbraham (1848) discovered overshoot on Page 198. Paper forgotten until noted by Burkhardt in 1908.
• Michelson's Oct 6 note started a series of comments by A. E. H. Love and Gibbs based on his device that could compute and re-synthesize the Fourier series, A New Harmonic Analyzer. See Michelson's Harmonic Analyzer. See the book.
• It was coined Gibbs Phenomenon by Bocher in 1906 [ Introduction to the theory of Fourier's series, online p 129] also according to him in his 1914 paper.
• Notes on the History of the Gibbs Phenomenon - by R. L. Herman. This has links to Fourier's memoir and to the series of letters that were inspired by A. Michelson's note.