Table of Contents

I. Introduction

Part 1. Historical Introduction

Part 2. Some Basic Concepts of the theory of sets

Part 3. A set of Axioms  for the Real-Number System

Part 4. Mathematical Induction, Summation Notation,and Related Topics

1. The Concepts of Integral Calculus

2. Some Applications of Integration

3. Continuous Functions

4. Differential Calculus

5. The Relation Between Integration and Differentiation

6. The Logarithm,the Exponential,and the Inverse Trigonmetric Functions

7. Polynomial Approximations to Functions

8. Introduction to Differential Equations

9. Complex Numbers

10. Sequences, Infinite Series, Improper Integrals

11. Sequences and Series of functions

12. Vector algebra

13. Applications of Vector Algebra to Analytic Geometry

14. Calculus of Vector Valued Functions

15. Linear Spaces

16. Linear Transformations and Matrices

Answers to exercises 617

Index 657

About the Author

TOM M. APOSTOL, Emeritus Professor at the California Institute of Technology, is the author of several highly regarded texts on calculus, analysis, and number theory, and is Director of Project MATHEMATICS!, a series of computer-animated mathematics videotapes.