Walter Craig

Does entropy really increase no matter what we do? Can light pass through a Big Bang? What is certain about the Heisenberg uncertainty principle? Many laws of physics are formulated in terms of differential equations, and the questions above are about the nature of their solutions. This book puts together the three main aspects of the topic of partial differential equations, namely theory, phenomenology, and applications, from a contemporary point of view. In addition to the three principal examples of the wave equation, the heat equation, and Laplace's equation, the book has chapters on dispersion and the Schrodinger equation, nonlinear hyperbolic conservation laws, and shock waves. The book covers material for an introductory course that is aimed at beginning graduate or advanced undergraduate level students. Readers should be conversant with multivariate calculus and linear algebra. They are also expected to have taken an introductory level course in analysis. Each chapter includes a comprehensive set of exercises, and most chapters have additional projects, which are intended to give students opportunities for more in-depth and open-ended study of solutions of partial differential equations and their properties.

The role of therapy in schools is a topic that has been significantly under-researched and often overlooked. Considering the number of students in full-time education with serious emotional and behavioural difficulties, the skills and tricks used by therapists can be usefully passed on to teachers in the classroom. This book traces a substantial four-year project that applied the principles of therapeutic education in one school setting and exposed how current educational contexts actually contribute to disaffection and disruption of young people's learning. The authors propose a practical model of school and curricular experience, based on therapeutic relationships, that has led to outstanding positive results in school development. With suugestions throughout for tried-and-tested strategies that really work, this book will help professionals turn troubled young people's experience of education from the nightmare it often is, into an adventure with positive results for lifelong learning.