Introduction to Partial Differential Equations and Hilbert Space Methods

Karl E. Gustafson

Introduction to Partial Differential Equations and Hilbert Space Methods provides an outstanding introduction to the fundamental concepts, methods, and applications of partial differential equations that is appropriate for undergraduate students.

Within practical mathematics, the first chapter provides a comprehensive introduction to partial differential equations and the Fourier series. This approach is then developed further in the contexts of Hilbert space and numerical methods in the following chapter, which begins with a more in-depth examination of the primary method for solving partial differential equations, which is the separation of variables and continues with a discussion of how this method can be applied. An enlarged study of first-order systems, a brief introduction to computational methods, and parts of current research on the partial differential equations of fluid dynamics are included in chapter 3.

This outstanding, user-friendly work is perfect for a one-semester or full-year course because it contains more than 600 problems and exercises, explanations, examples, and a particular section of answers, hints, and solutions. This work will also provide a fascinating review of the subject’s fundamentals for mathematically curious laypeople.