This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added.
Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis...
This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most rece...
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise. Within each section the author creates a narrative that answers the five questions:
What is the scientific problem we are trying to understand?
How do we model that with...
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the mos...
