Linear Partial Differential Equations and Fourier Theory

This highly visual introductory textbook presents an in-depth treatment suitable for undergraduates in mathematics and physics, gradually introducing abstraction while always keeping the link to physical motivation. Designed for lecturers as well as students, downloadable files for all figures, exercises, and practice problems are available online, as are solutions.

Do you want a rigorous book that remembers where PDEs come from and what they look like? This highly visual introduction to linear PDEs and initial/boundary value problems connects the math to physical reality, all the time providing a rigorous mathematical foundation for all solution methods. Readers are gradually introduced to abstraction – the most powerful tool for solving problems – rather than simply drilled in the practice of imitating solutions to given examples. The book is therefore ideal for students in mathematics and physics who require a more theoretical treatment than given in most introductory texts. Also designed with lecturers in mind, the fully modular presentation is easily adapted to a course of one-hour lectures, and a suggested 12-week syllabus is included to aid planning. Downloadable files for the hundreds of figures, hundreds of challenging exercises, and practice problems that appear in the book are available online, as are solutions.