Advanced Calculus

Advanced Calculus: Theory and Practice, Second Edition offers a text for a one- or two-semester course on advanced calculus or analysis. The text improves students’ problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts, and helps them understand the connections among different topics.

The book explains how various topics in calculus may seem unrelated but have common roots. Emphasizing historical perspectives, the text gives students a glimpse into the development of calculus and its ideas from the age of Newton and Leibniz to the twentieth century. Nearly 300 examples lead to important theorems.

Features of the Second Edition:

• Improved Organization. Chapters are reorganized to address common preferences.
• Enhanced Coverage of Axiomatic Systems. A section is added to include Peano’s system of axioms for the set of natural numbers and their use in developing the well-known properties of the set N.
• Expanded and Organized Exercise Collection. There are close to 1,000 new exercises, many of them with solutions or hints. Exercises are classified based on the level of difficulty. Computation-oriented exercises are paired and solutions or hints provided for the odd-numbered questions.
• Enrichment Material. Historical facts and biographies of over 60 mathematicians.
• Illustrations. Thirty-five new illustrations are added in order to guide students through examples or proofs.

Table of Contents

1 Real Numbers

2 Sequences and Their Limits

3 Continuity

4 Derivative

5 Indefinite Integral

6 Definite Integral

7 Infinite Series

8 Sequences and Series of Functions

9 Fourier Series

10 Functions of Several Variables

11 Derivatives of Functions of Several Variables

12 Implicit Functions and Optimization

13 Integrals Depending on a Paramete-r

14 Integration in Rn

15 Fundamental Theorems of Multivariable Calculus

16 Solutions and Answers to Selected Exercises

About the Author

John Srdjan Petrovic is a professor at Western Michigan University.