This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires high motivation from the reader to work out the exercises. The reader is given the opportunity to discover important developments of the subject and to quickly arrive at the point of independent research. The compactness of the volume and the reputation of the author lends this consider set of problems to be a 'classic' in the making. This text is highly recommended for us as supplementary material for 3 graduate level courses.
A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.
A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair portion of the material have in the past been able to use the theory on their own applications and also gain an appreciation of the possibility of a rather comprehensive point of view on the subject of partial differential equations.
The use of difference matrices and high-level MATLAB® commands to implement finite difference algorithms is pedagogically novel. This unique and concise textbook gives the reader easy access and a general ability to use first and second difference matrices to set up and solve linear and nonlinear systems in MATLAB which approximate ordinary and partial differential equations. Prerequisites include a knowledge of basic calculus, linear algebra, and ordinary differential equations. Some knowledge of partial differential equations is a plus though the text may easily serve as a supplement for the student currently working through an introductory PDEs course. Familiarity with MATLAB is not required though a little prior experience with programming would be helpful. In addition to its special focus on solving in MATLAB, the abundance of examples and exercises make this text versatile in use. It would serve well in a graduate course in introductory scientific computing for partial differential equations. With prerequisites mentioned above plus some elementary numerical analysis, most of the material can be covered and many of the exercises assigned in a single semester course. Some of the more challenging exercises make substantial projects and relate to topics from other typical graduate mathematics courses, e.g., linear algebra, differential equations, or topics in nonlinear functional analysis. A selection of the exercises may be assigned as projects throughout the semester. The student will develop the skills to run simulations corresponding to the primarily theoretical course material covered by the instructor. The book can serve as a supplement for the instructor teaching any course in differential equations. Many of the examples can be easily implemented and the resulting simulation demonstrated by the instructor. If the course has a numerical component, a few of the more difficult exercises may be assigned as student projects. Established researchers in theoretical partial differential equations may find this book useful as well, particularly as an introductory guide for their research students. Those unfamiliar with MATLAB can use the material as a reference to quickly develop their own applications in that language. Practical assistance in implementing algorithms in MATLAB can be found in these pages. A mathematician who is new to the practical implementation of methods for scientific computation in general can learn how to implement and execute numerical simulations of differential equations in MATLAB with relative ease by working through a selection of exercises. Additionally, the book can serve as a practical guide in independent study, undergraduate or graduate research experiences, or for reference in simulating solutions to specific thesis or dissertation-related experiments.
The reasons, methods, and outcomes of system change in general, and in Russia and Eastern Europe in particular are analyzed, using the analytical apparatus developed in the monograph.
This volume contains the proceedings of the conference on Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms. It presents current research in variational methods as applied to nonlinear elliptic PDE, although several articles concern nonlinear PDE that are nonvariational and/or nonelliptic. The book contains both survey and research papers discussing important open questions and offering suggestions on analytical and numerical techniques for solving those open problems. It is suitable for graduate students and research mathematicians interested in elliptic partial differential equations.
First published in 1994. The reasons, methods, and outcomes of system change in general, and in Russia and Eastern Europe in particular are analyzed, using the analytical apparatus developed in the monograph.
Meditations, devotions, and prayers selected from the collection gathered together and published after Newman's death. Often surprisingly simple and direct, they combine the traditional language of Catholic devotion with Newman's own distinct voice. +
As one of the most outstanding Christian thinkers in history, John Henry Newman continues to influence theology, especially Catholic theology, long after his death in 1890. Yet, his writings on faith, particularly The Grammar of Assent, are difficult to read without guidance and direction.
John Bachman (1790-1874) was an internationally renowned naturalist and a prominent Lutheran minister. This is the first collection of his writings, containing selections from his three major books, his letters, and his articles on plants and animals, education, religion, agriculture, and the human species. Bachman was the leading authority on North American mammals. He was responsible for the descriptions of the 147 mammal species included in Viviparous Quadrupeds of North America, a massive work produced in collaboration with John James Audubon. Bachman relied entirely on scientific evidence in his work and was exceptional among his fellow naturalists for studying the whole of natural history. Bachman also relied on scientific evidence in his Doctrine of the Unity of the Human Race. He showed that human beings constitute a single species that developed as varieties equivalent to the varieties of domesticated animals. In this work, perhaps his most significant accomplishment, Bachman stood nearly alone in challenging the polygenetic views of Louis Agassiz and others that white and black people descended from different progenitors. Bachman was also an important figure in the establishment of Lutheranism in the Southeast. He wrote the first American monograph on the doctrines of Martin Luther and the history of the Reformation. Bachman served for fifty-six years as minister of St. John's Lutheran Church in Charleston, South Carolina, and was one of the founders of Newberry College.
Two centuries after Lewis and Clark paddled down the Columbia Gorge so vividly pictured on the books cover, Jack Beattys memoir describes how young veterans of WW II moved into Oregons political life, revived the Democratic party, cooperated with young Republicans and forced legislative reapportionment. Months later Beatty defended the constitutional amendment from legal challenge. As counsel to the Democratic Party and later as a lawyer Jack dealt with Oregons two combustible Democratic senators, Wayne Morse and Richard L. Neuberger, then with Senator Maureen Neyberger elected to succeed her husband following his untimely death. Beatty suggested Sidney I. Lezak as Oregons U.S. Attorney to Congresswoman Edith Green. Lezaks appointment was famously blocked by Senator Maureen Neuberger for a year. Practicing law, co-chairing Robert Kennedys Oregon campaign for the presidency, Beatty served six years on the Portland School Board leading that urban district through the difficult late sixties. Governor Tom McCall appointed him to the Circuit Court, Governor Robert Straub appointed him to his Task Force on Corrections which proposed major changes in criminal law. Chief Justice Denecke made Judge Beatty legislative spokesman for the Judicial Conference and vice chair of the Commission for the Judicial Branch in the great restructuring of Oregons courts in the 1980s. Retiring from the court in 1985, Beatty served until 1990 as Vice Chair of the Criminal Justice Council under former Speaker Hardy Meyers in a massive reformation of Oregons criminal sentencing process. In 1996 Judge Beatty chared a Portland City Club study of the Oregon Initiative which proposed major limitations to that constitutional process. A candid description of history in the making, this memoir is also a concise description of the role of judging and the complex problems of our criminal justice system.
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