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Global Calculus

2005 Mathematics
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Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 028/5 ( reviews)

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Book Synopsis Global Calculus by : S. Ramanan

Download or read book Global Calculus written by S. Ramanan. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: The power that analysis, topology and algebra bring to geometry has revolutionised the way geometers and physicists look at conceptual problems. Some of the key ingredients in this interplay are sheaves, cohomology, Lie groups, connections and differential operators. In Global Calculus, the appropriate formalism for these topics is laid out with numerous examples and applications by one of the experts in differential and algebraic geometry. Ramanan has chosen an uncommon but natural path through the subject. In this almost completely self-contained account, these topics are developed from scratch. The basics of Fourier transforms, Sobolev theory and interior regularity are proved at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex. Many new perspectives on traditional and modern questions of differential analysis and geometry are the hallmarks of the book. The book is suitable for a first year graduate course on Global Analysis.

Global Pseudo-differential Calculus on Euclidean Spaces

2011-01-30 Mathematics
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Release : 2011-01-30
Genre : Mathematics
Kind : eBook
Book Rating : 12X/5 ( reviews)

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Book Synopsis Global Pseudo-differential Calculus on Euclidean Spaces by : Fabio Nicola

Download or read book Global Pseudo-differential Calculus on Euclidean Spaces written by Fabio Nicola. This book was released on 2011-01-30. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a global pseudo-differential calculus in Euclidean spaces, which includes SG as well as Shubin classes and their natural generalizations containing Schroedinger operators with non-polynomial potentials. This calculus is applied to study global hypoellipticity for several pseudo-differential operators. The book includes classic calculus as a special case. It will be accessible to graduate students and of benefit to researchers in PDEs and mathematical physics.

Multivariable Calculus

2012 Mathematics
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Release : 2012
Genre : Mathematics
Kind : eBook
Book Rating : 475/5 ( reviews)

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Book Synopsis Multivariable Calculus by : David Damiano

Download or read book Multivariable Calculus written by David Damiano. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: Written for mathematics, science, and engineering majors who have completed the traditional two-term course in single variable calculus, Multivariable Calculus bridges the gap between mathematical concepts and their real-world applications outside of mathematics. The ideas of multivariable calculus are presented in a context that is informed by their non-mathematical applications. It incorporates collaborative learning strategies and the sophisticated use of technology, which asks students to become active participants in the development of their own understanding of mathematical ideas. This teaching and learning strategy urges students to communicate mathematically, both orally and in writing. With extended examples and exercises and a student-friendly accessible writing style, Multivariable Calculus is an exciting and engaging journey into mathematics relevant to students everyday lives.

Mathematics and the Physical World

2012-03-15 Mathematics
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Release : 2012-03-15
Genre : Mathematics
Kind : eBook
Book Rating : 310/5 ( reviews)

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Book Synopsis Mathematics and the Physical World by : Morris Kline

Download or read book Mathematics and the Physical World written by Morris Kline. This book was released on 2012-03-15. Available in PDF, EPUB and Kindle. Book excerpt: Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

Advanced Calculus (Revised Edition)

2014-02-26 Mathematics
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Release : 2014-02-26
Genre : Mathematics
Kind : eBook
Book Rating : 952/5 ( reviews)

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Book Synopsis Advanced Calculus (Revised Edition) by : Lynn Harold Loomis

Download or read book Advanced Calculus (Revised Edition) written by Lynn Harold Loomis. This book was released on 2014-02-26. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

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