Lectures on the Hyperreals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on the Hyperreals write by Robert Goldblatt. This book was released on 2012-12-06. Lectures on the Hyperreals available in PDF, EPUB and Kindle. An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.
Non-standard Analysis
Non-standard Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Non-standard Analysis write by Abraham Robinson. This book was released on 2016-08-11. Non-standard Analysis available in PDF, EPUB and Kindle. Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
Distributions and Operators
Distributions and Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Distributions and Operators write by Gerd Grubb. This book was released on 2008-10-10. Distributions and Operators available in PDF, EPUB and Kindle. This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises and examples.
Model-Based Reasoning in Science, Technology, and Medicine
Model-Based Reasoning in Science, Technology, and Medicine - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Model-Based Reasoning in Science, Technology, and Medicine write by Lorenzo Magnani. This book was released on 2007-06-30. Model-Based Reasoning in Science, Technology, and Medicine available in PDF, EPUB and Kindle. The volume is based on papers presented at the international conference on Model-Based Reasoning in Science and Medicine held in China in 2006. The presentations explore how scientific thinking uses models and explanatory reasoning to produce creative changes in theories and concepts. The contributions to the book are written by researchers active in the area of creative reasoning in science and technology. They include the subject area’s most recent results and achievements.
Nonstandard Methods and Applications in Mathematics
Nonstandard Methods and Applications in Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonstandard Methods and Applications in Mathematics write by Nigel J. Cutland. This book was released on 2017-03-30. Nonstandard Methods and Applications in Mathematics available in PDF, EPUB and Kindle. Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-fifth publication in the Lecture Notes in Logic series, grew from a conference on Nonstandard Methods and Applications in Mathematics held in Pisa, Italy from 12–16 June, 2002. It contains ten peer-reviewed papers that aim to provide something more timely than a textbook, but less ephemeral than a conventional proceedings. Nonstandard analysis is one of the great achievements of modern applied mathematical logic. These articles consider the foundations of the subject, as well as its applications to pure and applied mathematics and mathematics education.
