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

Links to the available resources. 

Note that the Mathematica notebooks may download as text files that may need to be pasted into a Mathematica notebook in order to be read.The Maple code is on .docx files from which it can be copied.

Chapter 1: Crises in Mathematics: Fourier's Series

• The Derivation of Fourier's Solution

• Laplace's Equation

• Finding the Coefficients

• Approximating Fourier's Solution

  • Mathematica code​

  • Maple code

• The General Solution

• The Orthogonality Relation

• Fourier Series as Complex Power Series

• Maple code for exercises

• Mathematica code for exercises

Chapter 2: Infinite Summations

• The quadrature of a parabolic segment

• The Archimedean Principle

• Explorations of the alternating harmonic series

  • Mathematica code

  • Maple code

• Assigning values to divergent series

• More Pi

  • Mathematica code

  • Maple code

• Newton's formula

• Explorations of the Harmonic Series

• Euler's Solution to the Vibrating Drumhead

• Explorations of d'Alembert's series

  • Mathematica code

  • Maple code

• Explorations of Lagrange's Remainder

  • Mathematica code

  • Maple code

• Maple code for exercises

• Mathematica code for exercises

Chapter 3: Differentiability and Continuity

• Newton-Raphson Method

• How to find and write a proof

• Continued Fractions

• The Marquis de l'Hospital

• Maple code for exercises

• Mathematica code for exercises

Chapter 4: The Convergence of Infinite Series

• Stirling's Formula

  • Mathematica code

  • Maple code

• Exponential function

  • Mathematica code

  • Maple code

• Convergence in norm

• Gauss's test

• Maple code for exercises

• Mathematica code for exercises

Chapter 5: Understanding Infinite Series

• The Dilogarithm

• Maple code for exercises

• Mathematica code for exercises

Chapter 6: Return to Fourier Series​

• Maple code for exercises

• Mathematica code for exercises

Appendix A: Explorations of the Infinite

• Binomial coefficients and sums of nth powers

• Maple code for exercises

• Mathematica code for exercises

Corrections

Acknowledgements