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Real Analysis: An Undergraduate Problem Book for Mathematicians, Applied Scientists, and Engineers is a classical Real Analysis/Calculus problem book. This topic has been a compulsory subject for every undergraduate studying mathematics or engineering for a very long time. This volume contains a huge number of engaging problems and solutions, as well as detailed explanations of how to achieve these solutions. This latter quality is something that many problem books lack, and it is hoped that this feature will be useful to students and instructors alike. Features Hundreds of problems and solutions Can be used as a stand-alone problem book, or in conjunction with the author’s textbook, Real Analysis: An Undergraduate Textbook for Mathematicians, Applied Scientists, and Engineers, ISBN 9781032481487 Perfect resource for undergraduate students studying a first course in Calculus or Real Analysis Contains explanatory figures, detailed techniques, tricks, hints, and “recipes” on how to proceed once we have a calculus problem in front of us.
In the history of mathematics there are many situations in which cal- lations were performed incorrectly for important practical applications. Let us look at some examples, the history of computing the number ? began in Egypt and Babylon about 2000 years BC, since then many mathematicians have calculated ? (e. g. , Archimedes, Ptolemy, Vi` ete, etc. ). The ?rst formula for computing decimal digits of ? was disc- ered by J. Machin (in 1706), who was the ?rst to correctly compute 100 digits of ?. Then many people used his method, e. g. , W. Shanks calculated ? with 707 digits (within 15 years), although due to mistakes only the ?rst 527 were correct. For the next examples, we can mention the history of computing the ?ne-structure constant ? (that was ?rst discovered by A. Sommerfeld), and the mathematical tables, exact - lutions, and formulas, published in many mathematical textbooks, were not veri?ed rigorously [25]. These errors could have a large e?ect on results obtained by engineers. But sometimes, the solution of such problems required such techn- ogy that was not available at that time. In modern mathematics there exist computers that can perform various mathematical operations for which humans are incapable. Therefore the computers can be used to verify the results obtained by humans, to discovery new results, to - provetheresultsthatahumancanobtainwithoutanytechnology. With respectto our example of computing?, we can mention that recently (in 2002) Y. Kanada, Y. Ushiro, H. Kuroda, and M.
This book presents mathematical tools to solve partial differential equations, typical of physical problems. It explains in a detailed manner the process of solving the problems that typically arise in the context of physics. Although there are a large number of textbooks on this topic, few go so deep into the topic. One of the original and unique features of this book is emphasis on the mathematical formulation of the problems, as well as the analysis of several alternative ways to solve them. Importantly, the book provides a graphical analysis of the results when appropriate. It describes a wide scope of the problems, with detailed solutions and the methods involved, ranging from cases in one to three dimensions, from Cartesian to polar, cylindrical, and spherical coordinates and includes properties and applications of the Fourier transform to solve partial differential equations.
Publishes papers reporting on research and development in optical science and engineering and the practical applications of known optical science, engineering, and technology.
More than 40 million books sold in the Schaum's Outline series!
This book is designed to introduce the reader to the field of NMR/MRI at very low magnetic fields, from milli-Tesla to micro-Tesla, the ultra-low field (ULF) regime. The book is focused on applications to imaging the human brain, and hardware methods primarily based upon pre-polarization methods and SQUID-based detection. The goal of the text is to provide insight and tools for the reader to better understand what applications are best served by ULF NMR/MRI approaches. A discussion of the hardware challenges, such as shielding, operation of SQUID sensors in a dynamic field environment, and pulsed magnetic field generation are presented. One goal of the text is to provide the reader a framework of understanding the approaches to estimation and mitigation of low signal-to-noise and long imaging time, which are the main challenges. Special attention is paid to the combination of MEG and ULF MRI, and the benefits and challenges presented by trying to accomplish both with the same hardware. The book discusses the origin of unique relaxation contrast at ULF, and special considerations for image artifacts and how to correct them (i.e. concomitant gradients, ghost artifacts). A general discussion of MRI, with special consideration to the challenges of imaging at ULF and unique opportunities in pulse sequences, is presented. The book also presents an overview of some of the primary applications of ULF NMR/MRI being pursued.