Ideal for the 1-term course, A Journey into Partial Differential Equations provides a solid introduction to PDEs for the undergraduate math, engineering, or physics student. Discussing underlying physics, concepts and methodologies, the text focuses on the classical trinity of equations: the wave equation, heat/diffusion equation, and Laplace's equation. Bray provides careful treatment of the separation of variables and the Fourier method, motivated by the geometrical notion of symmetries and places emphasis on both the qualitative and quantitative methods, as well as geometrical perspectives. With hundred of exercises and a wealth of figures, A Journey into Partial Differential Equations proves to be the model book for the PDE course.
Unfolding Ideas via Examples | First Order Linear PDE | The Classical Trinity Revisited | An Introduction to Distributions | Fourier Expansions | Diffusion & Waves with Boundaries | Laplace’s Equation | Fourier Expansions on a Sphere