The calculus of variations is a beautiful subject with a rich history and with origins in the minimization problems of calculus. Although it is now at the core of many modern mathematical fields, it does not have a well-defined place in most undergraduate mathematics curricula. This volume should nevertheless give the undergraduate reader a sense of its great character and importance. Interesting functionals, such as area or energy, often give rise to problems whose most natural solution occurs by differentiating a one-parameter family of variations of some function. The critical points of the functional are related to the solutions of the associated Euler-Lagrange equation. These differential equations are at the heart of the calculus of variations and its applications to wave mechanics, minimal surfaces, soap bubbles, and modeling traffic flow. All are readily accessible to advanced undergraduates. This book is derived from a workshop sponsored by Rice University. It is suitable for advanced undergraduates, graduate students and research mathematicians interested in the calculus of variations and its applications to other subjects.

The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical software. It is suitable for an undergraduate or beginning graduate course, or for self study. It provides excellent preparation for more advanced books and courses on the calculus of variations and optimal control theory.

A publication of the American Brahms Society, Brahms Studies publishes essays on the life, work, and artistic milieu of Johannes Brahms. Each volume collects the best in Brahms scholarship, including criticism, analysis, theory, biography, archival and documentary studies, and translations of important studies that have appeared in foreign languages.

This carefully graded, pedagogical performance edition contains 12 outstanding classical sonatas by Haydn, Mozart and Beethoven. Each sonata appears in its original form and comes complete with performance notes and clearly presented editorial markings.

This Companion constitutes the most significant and comprehensive reference source to the composer in English. Edited by two of the leading scholars in the field, the collection consists of over 50 contributions from an international array of contributors, including recognized Polish experts. The Companion thus provides a systematic, authoritative and up-to-date compilation of information concerning the composer's life, thought and works.

Organizational Change: Themes and Issues presents a critical approach to organizational change, viewing change as a series of critical reflections rather than a series of recipes or models.

Mathematical modelling and simulation is an increasingly powerful area of mathematics and computer science, which in recent years has been fuelled by the unprecedented access to larger than ever stores of data. These techniques have an increasing number of applications in the professional and political spheres, and people try to predict the results of certain courses of action as accurately as possible. Computing Possible Futures explores the use of models on everyday phenomena such as waiting in lines and driving a car, before expanding the model's complexity to look at how large-scale computational models can help imagine big scale " scenarios like the effect self-driving cars on the US economy. The successes and failures of complex real world problems are examined, and it is shown how few, if any, failures are due to model errors or computational difficulties. It is also shown how real life decision makers have addressed important problems and used their model-based understanding of possible futures to inform these decisions. Written in an entertaining and accessible way, Computing Possible Futures will help those concerned about the futurity of their decisions to understand what fundamentally needs to be done, why it needs to be done, and how to do it.

Amid civil war, failing states, and terrorism, Arab liberals are growing in numbers and influence. Advocating a culture of equity, tolerance, good governance, and the rule of law, they work through some of the region’s largest media outlets to spread their ideals within the culture. Broadcasting Change analyzes this trend by portraying the intersection of media and politics in two Arab countries with seismic impact on the region and beyond. In Saudi Arabia, where hardline clerics silenced their opponents for generations, liberals now dominate the airwaves. Their success in weakening clerics’ grip over the public space would not only help develop the country; it would ensure that the birthplace of the prophet Muhammad exports a constructive understanding of Islam. In Egypt, home to a brutal government crackdown on Islamists and a bloodsport of attacks on Coptic Christians, local liberals are acting with courage on the ground and over the airwaves. Through TV talk shows, drama, and comedy, they play off the government’s anti-Islamist agenda to more thoughtfully advocate religious reform. Author Joseph Braude, himself a voice in Arabic-language broadcasts and publications, calls for international assistance to the region’s liberals, particularly in the realm of media. Local civic actors and some reform-minded autocrats welcome a new partnership with media experts and democratic governments in North America, Europe, and the Far East. Broadcasting Change argues that support for liberal reform through Arabic media should be construed as an international “public good” — on par with military peacekeeping and philanthropy.

This comprehensive nursing text has been fully and extensively updated for this third edition, and offers students a complete guide to the art and science of mental health nursing. The book combines theory and practice to look in-depth at: Different 'types' of mental health problems ; Different therapeutic interventions ; The practical tools of nursing such as risk, assessment, problem solving ; Key themes such as ethics, law and professional issues.