Lewin J. An Interactive Introduction to Mathematical Analysis

Cambridge University Press, 2003. — 530 p. — ISBN 0521815894.Интерактивное Введение в Математический АнализThis book provides a rigorous course in the calculus of functions of a real variable. Its gentle approach, particularly in its early chapters, makes it especially suitable for students who are not headed for graduate school. For those who are, this book gives an opportunity to engage in a penetrating study of real analysis. The companion onscreen version of this text contains hundreds of links to alternative approaches, more complete explanations and solutions to exercises; links that make it more friendly than any printed book could be. In addition, there are links to a wealth of optional material that an instructor can select for a more advanced course, and that students can use as a reference long after their first course has ended. The CD provides exercises that can be worked interactively with the help of the computer algebra systems that are bundled with Scientific Notebook.Background Material
The Emergence of Rigorous Calculus
Mathematical Grammar
Strategies for Writing Proofs
Elements of Set Theory
Elementary Concepts of Analysis
The Real Number System
Elementary Topology of the Real Line
Limits of Sequences
Limits and Continuity of Functions
Differentiation
The Exponential and Logarithmic Functions
The Riemann Integral
Infinite Series
Improper Integrals
Sequences and Series of Functions
Calculus of a Complex Variable (Optional)
Integration of Functions of Two Variables
Sets of Measure Zero (Optional)
Calculus of Sever
al Variables (Optional)