Partial Differential Equations

Wolfgang Arendt is Senior Professor of Analysis at Ulm University. His research areas are functional analysis and partial differential equations.Karsten Urban is Professor of Numerical Mathematics at Ulm University. His research interests include numerical methods for partial differential equations, especially with concrete applications in science and technology.

• 1 Modeling, or where do differential equations come from.- 2 Classification and characteristics.- 3 Elementary methods.- 4 Hilbert spaces.- 5 Sobolev spaces and boundary value problems in dimension one.- 6 Hilbert space methods for elliptic equations.- 7 Neumann and Robin boundary conditions.- 8 Spectral decomposition and evolution equations.- 9 Numerical methods.- 10 Maple®, or why computers can sometimes help.- Appendix.

“This book would make a good textbook because of the broad selection of material. The book devotes at least some space to every aspect of PDEs one might expect to see in an introductory graduate level course, and then some. An instructor wanting to emphasize one aspect or another may find enough material in the book. … The spectrum of material from concrete to abstract gives a well-rounded introduction to partial differential equations.” (John D. Cook, MAA Reviews, December 31, 2023)