Author: Victor Lenard ShapiroPublisher:
ISBN:
Category : Vector fields
Languages : en
Pages : 60
Book Description
The Divergence Theorem for Discontinuous Vector Fields
Author: Victor Lenard ShapiroPublisher:
ISBN:
Category : Vector fields
Languages : en
Pages : 60
Book Description
Advanced Calculus (Revised Edition)
Author: Lynn Harold LoomisPublisher: World Scientific Publishing Company
ISBN: 9814583952
Category : Mathematics
Languages : en
Pages : 595
Book Description
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.
The Divergence Theorem Without Differentiability Conditions
Author: Victor Lenard ShapiroPublisher:
ISBN:
Category : Divergence theorem
Languages : en
Pages : 8
Book Description
Differential Forms and Applications
Author: Manfredo P. Do CarmoPublisher: Springer Science & Business Media
ISBN: 3642579515
Category : Mathematics
Languages : en
Pages : 124
Book Description
An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.
APEX Calculus
Author: Gregory HartmanPublisher:
ISBN: 9781514225158
Category : Calculus
Languages : en
Pages : 0
Book Description
APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).
Proceedings of the National Academy of Sciences of the United States of America
Author: National Academy of Sciences (U.S.)Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 1174
Book Description
The Proceedings of the National Academy of Sciences (PNAS) publishes research reports, commentaries, reviews, colloquium papers, and actions of the Academy. PNAS is a multidisciplinary journal that covers the biological, physical, and social sciences.
Partial Differential Equations
Author: Walter A. StraussPublisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467
Book Description
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Calculus on Manifolds
Author: Michael SpivakPublisher: Westview Press
ISBN: 9780805390216
Category : Science
Languages : en
Pages : 164
Book Description
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
Annals of Mathematics
Author: AFOSR.
Author: United States. Air Force. Office of Scientific ResearchPublisher:
ISBN:
Category : Research
Languages : en
Pages : 1136
Book Description