Calculus

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 engaged in preparing the seventh editions of his textbooks and pursuing his interest in the Linux operating system.   Dr. Christopher Essex. is Director, Program in Theoretical Physics, and Professor of Applied Mathematics, Department of Applied Mathematics at the University of Western Ontario.

Preface
To the Student
To the Instructor
Acknowledgements
What Is Calculus?
Preliminaries
Chapter 1:Limits and Continuity
Chapter 2:Differentiation
Chapter 3:Transcendental Functions
Chapter 4:Some 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:Ordinary Differential Equations
Answers to Odd-Numbered Exercises
Appendix I:Complex Numbers
Appendix II:Complex Functions
Appendix III:Continuous Functions
Appendix IV:The Riemann Integral
Appendix V:Doing Calculus with Maple
Index