Global Calculus
Title | Global Calculus PDF eBook |
Author | S. Ramanan |
Publisher | American Mathematical Soc. |
Pages | 330 |
Release | 2005 |
Genre | Mathematics |
ISBN | 0821837028 |
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
Title | Global Pseudo-differential Calculus on Euclidean Spaces PDF eBook |
Author | Fabio Nicola |
Publisher | Springer Science & Business Media |
Pages | 309 |
Release | 2011-01-30 |
Genre | Mathematics |
ISBN | 376438512X |
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
Title | Multivariable Calculus PDF eBook |
Author | David Damiano |
Publisher | Jones & Bartlett Publishers |
Pages | 560 |
Release | 2012 |
Genre | Mathematics |
ISBN | 0763782475 |
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.
Advanced Calculus (Revised Edition)
Title | Advanced Calculus (Revised Edition) PDF eBook |
Author | Lynn Harold Loomis |
Publisher | World Scientific Publishing Company |
Pages | 595 |
Release | 2014-02-26 |
Genre | Mathematics |
ISBN | 9814583952 |
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.
Mathematics and the Physical World
Title | Mathematics and the Physical World PDF eBook |
Author | Morris Kline |
Publisher | Courier Corporation |
Pages | 514 |
Release | 2012-03-15 |
Genre | Mathematics |
ISBN | 0486136310 |
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
Title | Advanced Calculus PDF eBook |
Author | Ellen F. Buck |
Publisher | |
Pages | 622 |
Release | 1978 |
Genre | Calculus |
ISBN | 9780070850767 |
Descartes' Dream
Title | Descartes' Dream PDF eBook |
Author | Philip J. Davis |
Publisher | Courier Corporation |
Pages | 354 |
Release | 2005-01-01 |
Genre | Mathematics |
ISBN | 0486442527 |
These provocative essays take a modern look at the 17th-century thinker's dream, examining the influences of mathematics on society, particularly in light of technological advances. They survey the conditions that elicit the application of mathematic principles; the applications' effectiveness; and how applied mathematics transform perceptions of reality. 1987 edition.