David Borthwick

Spectral Theory is a text covering basic functional analysis with an emphasis on spectral theory. The first half of the book introduces the theory of Hilbert spaces and operators, leading up to a proof of the spectral theorem. In the second half, this theory is applied to develop the spectral theory for some important examples, such as the Dirichlet Laplacian and Schrodinger operators. The text is published by Springer in the GTM series. Available directly from the publisher or from Amazon.

A current list of errata is available here. Please email me if you find an issue that is not on the list.

Introduction to Partial Differential Equations is a text for advanced undergraduate or beginning graduate course on PDE. My primary goal in this book was to make the theory accessible without requiring extensive analysis prerequisites. The text is published by Springer in the Universitext series. Available directly from the publisher or from Amazon.

A current list of errata is available here. Please email me if you find an issue that is not on the list. The first printing had additional mistakes which were corrected as of Spring 2018, in both print and online editions.

Spectral Theory of Infinite-Area Hyperbolic Surfaces has a second edition as of 2016, Volume 318 in the Progress in Mathematics series published by Birkhauser. Available directly from the publisher or from Amazon.

A current list of errata is available here.

Overtones and Musical Intervals, a video lecture on the mathematical origins of musical intervals and scales. This is an expanded and edited version of a presentation I did for the online Mathapalooza event at the 2021 Atlanta Science Festival.

A video featuring the 3rd movement from Phillip Glass: Symphony No. 3. The parts were all recorded remotely during the 2020 pandemic lockdown, and I did the arranging, mixing, and video production. I also cover 7 different viola parts, and joined by various family members and friends.