Short Route To Chaos

This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given. The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.

Covering the set texts in the AQA B specification, this title helps students make a smooth transition from GCSE to AS, then up to A2. It focuses on the AQA B Assessment Objectives at AS, and includes exam and coursework tips throughout that show students how to get the best grades.

This convenient teacher's guide includes perforated, three-hole punched assignments with answers, learning objectives, grading criteria, and short essay questions to help the student comprehend and apply the information presented. The following is included in this complete year of high school British history curriculum: The teacher text has the student questions organized at the back for easy use in testing and reviews The course has been designed with 34 chapters representing 34 weeks of study Each chapter has 5 lessons each, taking approximately 30 minutes a day The final lesson of the week is the exam covering the week's chapter A parent or teacher can grade assignments daily or weekly, and keep track of this in their files This course is designed for the student to practice independent learning. This is a solid educational process to help a student develop a Christian world view and form his/her own understanding of history.

This first historical account of the free school movement of the 1960s documents the formation of hundreds of small, independent schools across the United States that marked a turning point in American education. The book revisits and interprets the radical democratic educational vision behind those schools through the works of some of the authors of that time such as John Holt, A. S. Neill, Paul Goodman, and George Dennison. These authors—and the thousands of educators, parents, and young people who took part in the free school movement—passionately advocated for students' intellectual and psychological freedom, and for their autonomy and individuality in a society they saw as increasingly standardized and corporately managed. Although free school ideology was renounced during the conservative restoration of the 1970s and 1980s, and the once popular literature is now largely forgotten, Miller argues that radical educational critique is especially relevant in today's educational climate, in light of the standards movement, high stakes testing, school violence and its suppression, and corporate influence over the curriculum.

School choice has lately risen to the top of the list of potential solutions to America's educational problems, particularly for the poor and the most disadvantaged members of society. Indeed, in the last few years several states have held referendums on the use of vouchers in private and parochial schools, and more recently, the Supreme Court reviewed the constitutionality of a scholarship program that uses vouchers issued to parents. While there has been much debate over the empirical and methodological aspects of school choice policies, discussions related to the effects such policies may have on the nation's moral economy and civil society have been few and far between. School Choice, a collection of essays by leading philosophers, historians, legal scholars, and theologians, redresses this situation by addressing the moral and normative side of school choice. The twelve essays, commissioned for a conference on school choice that took place at Boston College in 2001, are organized into four sections that consider the relationship of school choice to equality, moral pluralism, institutional ecology, and constitutionality. Each section consists of three essays followed by a critical response. The contributors are Patrick McKinley Brennan, Charles L. Glenn, Amy Gutmann, David Hollenbach, S. J., Meira Levinson, Sanford Levinson, Stephen Macedo, John T. McGreevy, Martha Minow, Richard J. Mouw, Joseph O'Keefe, S. J., Michael J. Perry, Nancy L. Rosenblum, Rosemary C. Salomone, Joseph P. Viteritti, Paul J. Weithman, and Alan Wolfe.

This collection discusses conditions of social class and the ways in which class is produced in educational institutions and families, while simultaneously interrogating and challenging our understandings of social class as it is linked to race, gender, and nation.

This play charts the dramatic events leading to the execution of Sir Thomas More in 1535 and has been a modern stage classic since its first production in 1960. The author's previous plays include 'Flowering Cherry' and 'State of Revolution'.