Advanced Calculus: Theory and Practice

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.

About the Author:

John Srdjan Petrovic is a professor at Western Michigan University.

《高等微積分：理論與實踐，第二版》是一本適用於一學期或兩學期的高等微積分或分析課程的教材。本書旨在提升學生的問題解決和證明寫作能力，使他們熟悉微積分概念的歷史發展，並幫助他們理解不同主題之間的聯繫。

本書解釋了微積分中的各種主題可能看似無關，但實際上有共同的根源。強調歷史觀點，本書讓學生一窺從牛頓和萊布尼茲時代到二十世紀微積分及其思想的發展。近300個例子引導學生理解重要的定理。

第二版的特點包括：

- 改進的組織。章節重新組織以滿足常見的偏好。
- 增強的公理系統涵蓋。新增了一節，包括皮亞諾對自然數集合的公理系統及其在發展集合N的著名性質中的應用。
- 擴充並組織良好的習題集。近1000個新習題，其中許多有解答或提示。習題根據難度分類。計算導向的習題成對出現，奇數題提供解答或提示。
- 豐富的補充材料。包括60多位數學家的歷史事實和傳記。
- 插圖。新增了35個插圖，以引導學生理解例子或證明。

關於作者：
約翰·斯爾賈·佩特羅維奇（John Srdjan Petrovic）是西密歇根大學的教授。

John Srdjan Petrovic is a Professor at Western Michigan University.

John Srdjan Petrovic 是西密歇根大學的教授。