This textbook is suitable for two courses in computational physics. The first is at an advanced introductory level and is appropriate for seniors or first year graduate students. The student is introduced to integral and differential techniques, Monte Carlo integration, basic computer architecture, linear algebra, finite element techniques, digital signal processing and chaos. In this first part of the book, no knowledge of quantum mechanics is assumed. The third edition has expanded treatments of the subjects in each of the first nine chapters and a new section on modern parallel computing, in particular, Beowulf clusters.The second course (the last four chapters) deals with problems in the strong interaction using quantum mechanical techniques, with emphasis on solutions of many-body scattering problems and several-body bound state calculations with Monte Carlo techniques. It also contains a chapter dealing with the numerical summation of divergent series.
The use of computers to solve modern scientific problems is very widespread. The impact of the improvement of our techniques for the solution of complex problems is difficult to overstate. Even our approach to most problems has been changed. Solutions to problems once thought intractable are being routinely secured. Instead of using oversimplified models, as has been the practice for the treatment of scientific systems in the past, the entire problem can now be attacked. The second edition of Computation in Modern Physics develops and presents algorithms for the solution of many types of mathematical systems, some dating as far as the last few centuries, but also quite a number that have been developed within the last 10-50 years. In this last category, close attention is paid to the rapidly developing area of Monte Carlo techniques where new conceptual views of physics problems are being brought into play. With this method, problems in a large number of dimensions can be solved through the introduction of a modern method for the representation of multidimensional functions. This book is suitable for two different levels in computational physics. The first part is an advanced introductory level and is appropriate for good students with no previous experience in computational methods or any student with some experience. Here the student is introduced to integral and differential techniques, Monte Carlo integration, basic computer architecture, methods of linear algebra, finite element techniques, digital signal processing and chaos. The second part of the book is more specialized for problems in strong interaction with emphasis on solutions to many-body scattering problems andseveral-body bound state calculations with Monte Carlo techniques. It also contains a chapter dealing with techniques for the summation of divergent series.
The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.
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