E-Book Overview
This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.
E-Book Content
Undergraduate Texts in Mathematics Editors S. Axler K.A. Ribet Undergraduate Texts in Mathematics Abbott: Understanding Analysis. Anglin: Mathematics: A Concise History and Philosophy. Readings in Mathematics. Anglin/Lambek: The Heritage of Thales. Readings in Mathematics. Apostol: Introduction to Analytic Number Theory. Second edition. Armstrong: Basic Topology. Armstrong: Groups and Symmetry. Axler: Linear Algebra Done Right. Second edition. Beardon: Limits: A New Approach to Real Analysis. Bak/Newman: Complex Analysis. Second edition. Banchoff/Wermer: Linear Algebra Through Geometry. Second edition. Berberian: A First Course in Real Analysis. Bix: Conics and Cubics: A Concrete Introduction to Algebraic Curves. Brèmaud: An Introduction to Probabilistic Modeling. Bressoud: Factorization and Primality Testing. Bressoud: Second Year Calculus. Readings in Mathematics. Brickman: Mathematical Introduction to Linear Programming and Game Theory. Browder: Mathematical Analysis: An Introduction. Buchmann: Introduction to Cryptography. Second Edition. Buskes/van Rooij: Topological Spaces: From Distance to Neighborhood. Callahan: The Geometry of Spacetime: An Introduction to Special and General Relavitity. Carter/van Brunt: The Lebesgue– Stieltj