Geared toward those who have studied elementary calculus and intend to progress to more advanced mathematics, this book stresses concepts rather than techniques. It emphasizes the simplest setting of basic theorems so that students may progress from "one-space" to "n-space" calculus.
An introductory section by the author reviews the roles of sets, relations, and functions. Subsequent chapters explore real numbers, the limit concept, useful theorems, continuity, differentiability, and integrability. The author focuses on real-valued functions of a real variable. Considerations of complex numbers appear only in optional supplements to certain chapters, as well as in the final two chapters, which consist of in-depth explorations of sequences of functions and Fourier series. Each chapter features several helpful exercises.
Table of Contents
1. Sets, Relations, and Functions
2. The Real Numbers
3. The Limit Concept
4. Three Important Theorems
8. Sequences of Functions: An Existence Theorem in Differential Equations
9. Fourier Series
Symbols and Notation