Advanced Calculus / Edition 2

Advanced Calculus / Edition 2

by Patrick M. Fitzpatrick
ISBN-10:
0821847910
ISBN-13:
9780821847916
Pub. Date:
01/13/2009
Publisher:
American Mathematical Society
ISBN-10:
0821847910
ISBN-13:
9780821847916
Pub. Date:
01/13/2009
Publisher:
American Mathematical Society
Advanced Calculus / Edition 2

Advanced Calculus / Edition 2

by Patrick M. Fitzpatrick
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Overview

Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables. Special attention has been paid to the motivation for proofs. Selected topics, such as the Picard Existence Theorem for differential equations, have been included in such a way that selections may be made while preserving a fluid presentation of the essential material. Supplemented with numerous exercises, Advanced Calculus is a perfect book for undergraduate students of analysis.


Product Details

ISBN-13: 9780821847916
Publisher: American Mathematical Society
Publication date: 01/13/2009
Series: Pure and Applied Undergraduate Texts Series , #5
Edition description: New Edition
Pages: 590
Product dimensions: 6.40(w) x 9.30(h) x 1.10(d)

About the Author

Ernst Breisach is professor emeritus of history at Western Michigan University and the author of several books, including American Progressive History: An Experiment in Modernization and On the Future of History: The Postmodernist Challenge and Its Aftermath, both published by the University of Chicago Press.

Table of Contents

Preface 
Introduction

 
1  
The Emergence of Greek Historiography

 2
 The Era of the Polis and Its Historians

 3
 Reaching the Limits of Greek Historiography

 4
 Early Roman Historiography: Myths, Greeks, and the Republic

 5
 Historians and the Republic’s Crisis

 6
 Perceptions of the Past in Augustan and Imperial Rome

 7
 The Christian Historiographical Revolution

 8
 The Historiographical Mastery of New Peoples, States, and Dynasties

 9
 Historians and the Ideal of the Christian Commonwealth

 10
 Historiography’s Adjustment to Accelerating Change

 11
 Two Turning Points: The Renaissance and The Reformation

 12
 The Continuing Modification of Traditional Historiography

 13
 The Eighteenth-Century Quest for a New Historiography

 14
 Three National Responses

 15
 Historians as Interpreters of Progress and Nation—1

 16
 Historians as Interpreters of Progress and Nation—2

 17
 A First Prefatory Note to Modern Historiography

 18
 History and the Quest for a Uniform Science

 19
 The Discovery of Economic Dynamics

 20
 Historians Encounter the Masses

 21
 The Problem of World History

 22
 Historiography Between Two World Wars (1918–39)
 The Twentieth-Century Context
 Challenges to Historians
 Historicism: From Dominance to Crisis
 Historians and the War Guilt Debate

 23
 History Writing in Liberal Democracies (1918–39)
 American Historiography after the “Great War”
 England: Historiography in a Fading Empire
 French Historians: The Revolutionary Tradition and a New Vision of the Past 

 24
 Historiography and the Grand Ideologies  
 Italian Fascism and historiography (1922–43)  
 German Historians in the Weimar Republic and Hitler’s Reich  
 The Soviet Union: The Imagined Future as the Guide for History  

 25
 American Historiography after 1945  
 New Realities and Traditional Horizons  
 Historical Repercussions of America’s New Status  
 Historiography as Call for Reform  

 26
 History in the Scientific Mode  
 History in the Language of Numbers  
 Reshaping Economic History  
 Growing Dissent: Narrativism  
 Psychohistory: Promise and Problems  

 

 27
 Transformations in English and French Historiography  
 Voices in the War Guilt Debate  
 History Writing in Post-imperial England  
 Traditional and New French Historical Perspectives  

 28
 Marxist Historiography in the Soviet Union and Western Democracies  
 The Problems and the End of the Soviet Union’s Marxism  
 Marxist Historical Theory in the West  

 29
 Historiography in the Aftermath of Fascism  
 Historical Perspectives in Post-war Italy  
 History for and of a New Germany  

 30
 World History Between Vision and Reality  
 The Multiple Cultures Model  
 Progress and Westernization  
 World System Theories  

 31
 Historiography, Postmodernity and Prospects  
 Historiographical Adjustments to a Turbulent Context  
 History and Visions of a Postmodern Future  
 The New Cultural History  
 Prospects

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