Differential equations and their applications : an introduction to applied mathematics / Martin Braun

The two mayor changes of this new edition are described by the author in the preface as follows: “The first concerns the computer programs in this text. In keeping with recent trends in computer science, we have replaced all the APL programs with Pascal and C programs. The second change, in response to many readers' suggestions, is the inclusion of a new chapter (Chapter 6) on Sturm-Liouville boundary value problems. Our goal in this chapter is not to present a whole lot of technical material. Rather it is to show that the theory of Fourier series presented in Chapter 5 is not an isolated theory but is part of a much more general and beautiful theory which encompasses many of the key ideas of linear algebra. To accomplish this goal we have included some additional material from linear algebra. In particular, we have introduced the notions of inner product spaces and self-adjoint matrices, proven that the eigenvalues of a self-adjoint matrix are real, and shown that all self-adjoint matrices possess an orthonormal basis of eigenvectors. These results are at the heart of Sturm-Liouville theory”.

Index