Proven in North America and abroad, this classic text has earned a reputation for excellent accuracy and mathematical rigour. Previous editions have been praised for providing complete and precise statements of theorems, using geometric reasoning in applied problems, and for offering a range of applications across the sciences. Written in a clear, coherent, and readable form, Calculus: A Complete Course makes student comprehension a clear priority.
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The 9th edition, in addition to various corrections and refinements, fills in gaps in the treatment of differential equations from the 8th edition, with entirely new material. A linear operator approach to understanding differential equations is added. Also added is a refinement of the existing material on the Dirac delta function, and a full treatment of Laplace transforms. In addition, there is an entirely new section on phase plane analysis. The new phase plane section covers the classical treatment, if that is all one wants, but it goes much further for those who want more, now or later. It can set the reader up for dynamical systems in higher dimensions in a unique, lucid, and compact exposition. With existing treatments of various aspects of differential equations throughout the existing text, the 9th edition becomes suitable for a semester course in differential equations, in addition to the existing standard material suitable for four semesters of calculus.
Besides numerous improvements and clarifications throughout the book and tweakings of existing material such as consideration of probability densities with heavy tails in Section 7.8, and a less restrictive definition of the Dirac delta function in Section 16.1, there are two new sections in Chapter 18, one on Laplace Transforms (Section 18.7) and one on Phase Plane Analysis of Dynamical Systems (Section 18.9).
Calculus: a Complete Course, 9th Edition contains 19 chapters, P and 1—18, plus 5 Appendices. It covers the material usually encountered in a three- to five-semester real-variable calculus program, involving real-valued functions of a single real variable (differential calculus in Chapters 1—4 and integral calculus in Chapters 5—8), as well as vector-valued functions of a single real variable (covered in Chapter 11), real-valued functions of several real variables (in Chapters 12—14), and vector-valued functions of several real variables (in Chapters 15—17). Chapter 9 concerns sequences and series, and its position is rather arbitrary.
Chapter 10 contains necessary background on vectors and geometry in 3-dimensional space as well as some linear algebra that is useful, although not absolutely essential, for the understanding of subsequent multivariable material. Material on differential equations is scattered throughout he book, but Chapter 18 provides a compact treatment of ordinary differential equations (ODEs), which may provide enough material for a one-semester course on the subject.
Robert Adams joined the Mathematics Department at the University of British Columbia in 1966 after completing a Ph.D. in Mathematics at the University of Toronto. His research interests in analysis led to the 1975 publication of a monograph, Sobolev Spaces, by Academic Press. It remained in print for 23 years. A second edition, joint with his colleague Professor John Fournier, was published in 2003. Professor Adams's teaching interests led to the 1982 publication of the first of his many calculus texts by Addison Wesley. These texts are now used worldwide. With a keen interest in computers, mathematical typesetting, and illustration, in 1984 Professor Adams became the first Canadian author to typeset his own textbooks using TeX on a personal computer. Since then he has also done all the illustrations for his books using the MG software program that he developed with his colleague, Professor Robert Israel. Now retired from UBC, Professor Adams is currently pursuing his interest in the Linux operating system.
Dr. Christopher Essex is Professor and Associate Chair in the Department of Applied Mathematics at the University of Western Ontario. He is a former director of its Theoretical Physics Program. He is an award-winning teacher and author. In 2012-13 Chris has become the first ever Phi Beta Kappa Visiting Scholar from a Canadian university.
Dr. Essex did pioneering work on the thermodynamics of photon and neutrino radiation. Among many international invitations to speak on this topic, he has taught at the UNESCO advanced school in Udine, Italy, and in 2011 his work was featured at the Joint European Thermodynamics Conference held in Chemnitz, Germany. Professor Essex is also co-discoverer of the entropy production paradox of anomalous superdiffusion. He also discovered, while a guest of the Vatican, modern mathematics (Sierpinski triangles) embedded in the ancient floor tiles of the Sistine Chapel and elsewhere in the Vatican museum.
Professor Essex held an NSERC (Natural Sciences and Engineering Research Council of Canada) postdoctoral fellowship at the Canadian Climate Centre to work on its big climate model. He was first appointed to the governing council of NSERC in 2006 and reappointed in 2009.
His work also includes applications of dynamical systems theory, such as chaos cryptography, and recently the limits of modelling and computation, among other applications of mathematics.