Calculus: A Complete Course

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.

Front Matter

Chapter P: Preliminaries

Chapter 1: Limits and Continuity

Chapter 2: Differentiation

Chapter 3: Transcendental Functions

Chapter 4: More Applications of Derivatives

Chapter 5: Integration

Chapter 6: Techniques of Integration

Chapter 7: Applications of Integration

Chapter 8: Conics, Parametric Curves, and Polar Curves

Chapter 9: Sequences, Series, and Power Series

Chapter 10: Vectors and Coordinate Geometry in 3-Space

Chapter 11: Vector Functions and Curves

Chapter 12: Partial Differentiation

Chapter 13: Applications of Partial Derivatives

Chapter 14: Multiple Integration

Chapter 15: Vector Fields

Chapter 16: Vector Calculus

Chapter 17: Differential Forms and Exterior Calculus (New Chapter)

Chapter 18: Ordinary Differential Equations

Appendix I: Complex Numbers

Appendix II: Complex Functions

Appendix III: Continuous Functions

Appendix IV: The Riemann Integral

Appendix V: Doing Calculus with Maple

Answers to Odd Numbered Exercises

Index