Introduction to Partial Differential Equations (Universitext)

December 4, 2020
Introduction to Partial Differential Equations (Universitext)

This modern take on partial differential equations does notrequire knowledge beyond vector calculus and linear algebra. Theauthor focuses on the most important classical partial differentialequations, including conservation equations and theircharacteristics, the wave equation, the heat equation, functionspaces, and Fourier series, drawing on tools from analysis only asthey arise.Within each section the author creates a narrative that answersthe five questions:What is the scientific problem we are trying tounderstand?How do we model that with PDE?What techniques can we use to analyze the PDE?How do those techniques apply to this equation?What information or insight did we obtain by developing andanalyzing the PDE?The text stresses the interplay between modeling andmathematical analysis, providing a thorough source of problems andan inspiration for the development of methods.