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.

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  • Unpublished resolution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

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)