Second Year Calculus
Download Second Year Calculus full books in PDF, epub, and Kindle. Read online free Second Year Calculus ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : David M. Bressoud |
Publisher | : Springer Science & Business Media |
Total Pages | : 399 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461209595 |
Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.
Author | : Zbigniew H. Nitecki |
Publisher | : American Mathematical Society |
Total Pages | : 491 |
Release | : 2022-01-11 |
Genre | : Mathematics |
ISBN | : 1470466759 |
Calculus Deconstructed is a thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous exposure to calculus techniques but not to methods of proof. This book is appropriate for a beginning Honors Calculus course assuming high school calculus or a "bridge course" using basic analysis to motivate and illustrate mathematical rigor. It can serve as a combination textbook and reference book for individual self-study. Standard topics and techniques in single-variable calculus are presented in context of a coherent logical structure, building on familiar properties of real numbers and teaching methods of proof by example along the way. Numerous examples reinforce both practical and theoretical understanding, and extensive historical notes explore the arguments of the originators of the subject. No previous experience with mathematical proof is assumed: rhetorical strategies and techniques of proof (reductio ad absurdum, induction, contrapositives, etc.) are introduced by example along the way. Between the text and exercises, proofs are available for all the basic results of calculus for functions of one real variable.
Author | : Lynn Harold Loomis |
Publisher | : World Scientific Publishing Company |
Total 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.
Author | : James J. Callahan |
Publisher | : Springer Science & Business Media |
Total Pages | : 542 |
Release | : 2010-09-09 |
Genre | : Mathematics |
ISBN | : 144197332X |
With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.
Author | : David M Bressoud |
Publisher | : |
Total Pages | : 404 |
Release | : 1991-08-08 |
Genre | : |
ISBN | : 9781461209607 |
Author | : Ron Larson |
Publisher | : Cengage Learning |
Total Pages | : 0 |
Release | : 2002 |
Genre | : Calculus |
ISBN | : 9780618087600 |
A one-year course integrating precaluculus with the first semester of calculus.
Author | : Michael Spivak |
Publisher | : Westview Press |
Total Pages | : 164 |
Release | : 1965 |
Genre | : Science |
ISBN | : 9780805390216 |
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.
Author | : David Perkins |
Publisher | : MAA |
Total Pages | : 181 |
Release | : 2012-04-12 |
Genre | : Education |
ISBN | : 0883855755 |
The story of how calculus came to be, accessible to anyone with a basic knowledge of geometry and algebra.
Author | : Morris Kline |
Publisher | : Courier Corporation |
Total Pages | : 962 |
Release | : 2013-05-09 |
Genre | : Mathematics |
ISBN | : 0486134768 |
Application-oriented introduction relates the subject as closely as possible to science with explorations of the derivative; differentiation and integration of the powers of x; theorems on differentiation, antidifferentiation; the chain rule; trigonometric functions; more. Examples. 1967 edition.
Author | : George Bluman |
Publisher | : |
Total Pages | : 404 |
Release | : 2014-09-01 |
Genre | : |
ISBN | : 9781461211334 |