" . . . if a physical system is capable of supporting solitary wave motions then such motions will invariably arise from quite general excitations. " - T. Maxworthy (1980), pg. 52. The discover of nonlocal solitary waves is unknown and anonymous, but he or she lived in the dry north of Australia many millenia before the birth of writing. There, on the shores of the Gulf of Carpentaria, vast cylinders of cloud roll from northeast to southwest most mornings. Perhaps 300 meters in diameter, perhaps 500 meters above the ocean, these cylinders of cloud stretch from horizon to horizon. As the cloud...

The goal of this book is to teach spectral methods for solving boundary value, eigenvalue, and time-dependent problems. Although the title speaks only of Chebyshev polynomials and trigonometric functions, the book also discusses Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions. These notes evolved from a course I have taught the past five years to an audience drawn from half a dozen different disciplines at the University of Michigan: aerospace engineering, meteorology, physical oceanography, mechanical engineering, naval architecture, and nuclear engineering....