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Chapter 1: Crises in Mathematics: Fourier's Series

Chapter 2: Infinite Summations

Chapter 3: Differentiability and Continuity

Chapter 4: The Convergence of Infinite Series

Chapter 5: Understanding Infinite Series

Chapter 6: Return to Fourier Series

Appendix A: Explorations of the Infinite

Corrections

Acknowledgements

Resources for A Radical Approach to Real Analysis (2nd edition)

Chapter 1: Crisis in Mathematics: Fourier's Series

Additional material:

• The Derivation of Fourier's Solution
• Laplace's Equation
• Finding the Coefficients
• Approximating Fourier's Solution
• The General Solution
• The Orthogonality Relation
• Fourier Series as Complex Power Series

Maple, Mathematica, and Octave/Matlab code for exercises
(The Mathematica notebook may download as a text file that may need to be pasted into a Mathematica notebook in order to be read.The Maple code is on an html file from which it can be copied. The Octave/Matlab code is in a zip file. This code was supplied by Rachel Drummond, a graduate student at CU-Denver.)