Softcover ISBN:  9781470465018 
Product Code:  REALAPP.S 
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eBook ISBN:  9781470412142 
Product Code:  REALAPP.E 
List Price:  $49.00 
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Softcover ISBN:  9781470465018 
eBook: ISBN:  9781470412142 
Product Code:  REALAPP.S.B 
List Price:  $104.00 $79.50 
MAA Member Price:  $93.60 $71.55 
AMS Member Price:  $83.20 $63.60 
Softcover ISBN:  9781470465018 
Product Code:  REALAPP.S 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
eBook ISBN:  9781470412142 
Product Code:  REALAPP.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 
Softcover ISBN:  9781470465018 
eBook ISBN:  9781470412142 
Product Code:  REALAPP.S.B 
List Price:  $104.00 $79.50 
MAA Member Price:  $93.60 $71.55 
AMS Member Price:  $83.20 $63.60 

Book Details2005; 197 ppMSC: Primary 26; 49; 42; 83
Real Analysis and Applications starts with a streamlined, but complete, approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]."
The text not only provides clear, logical proofs, but also shows the student how to derive them. The excellent exercises come with select solutions in the back. This is a text that makes it possible to do the full theory and significant applications in one semester.
Frank Morgan is the author of six books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this applied version of his Real Analysis text, Morgan brings his famous direct style to the growing numbers of potential mathematics majors who want to see applications along with the theory.
The book is suitable for undergraduates interested in real analysis.
ReadershipUndergraduate students interested in real analysis and its applications.

Table of Contents

Front Cover

Contents

Preface

Part I: Real Numbers and Limits

Chapter 1: Numbers and Logic

Chapter 2: Infinity

Chapter 3: Sequences

Chapter 4: Subsequences

Chapter 5: Functions and Limits

Chapter 6: Composition of Functions

Part II: Topology

Chapter 7: Open and Closed Sets

Chapter 8: Compactness

Chapter 9: Existence of Maximum

Chapter 10: Uniform Continuity

Chapter 11: Connected Sets and the Intermediate Value Theorem

Chapter 12: The Cantor Set and Fractals

Part III: Calculus

Chapter 13: The Derivative and the Mean Value Theorem

Chapter 14: The Riemann Integral

Chapter 15: The Fundamental Theorem of Calculus

Chapter 16: Sequences of Functions

Chapter 17: The Lebesgue Theory

Chapter 18: Infinite Series Σ∞n=1 an

Chapter 19: Absolute Convergence

Chapter 20: Power Series

Chapter 21: The Exponential Function

Chapter 22: Volumes of nBalls and the Gamma Function

Part IV: Fourier Series

Chapter 23: Fourier Series

Chapter 24: Strings and Springs

Chapter 25: Convergence of Fourier Series

Part V: The Calculus of Variations

Chapter 26: Euler’s Equation

Chapter 27: First Integrals and the Brachistochrone Problem

Chapter 28: Geodesics and Great Circles

Chapter 29: Variational Notation, Higher Order Equations

Chapter 30: Harmonic Functions

Chapter 31: Minimal Surfaces

Chapter 32: Hamilton’s Action and Lagrange’s Equations

Chapter 33: Optimal Economic Strategies

Chapter 34: Utility of Consumption

Chapter 35: Riemannian Geometry

Chapter 36: NonEuclidean Geometry

Chapter 37: General Relativity

Partial Solutions toExercises

Greek Letters

Index

Back Cover


Additional Material

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Real Analysis and Applications starts with a streamlined, but complete, approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]."
The text not only provides clear, logical proofs, but also shows the student how to derive them. The excellent exercises come with select solutions in the back. This is a text that makes it possible to do the full theory and significant applications in one semester.
Frank Morgan is the author of six books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this applied version of his Real Analysis text, Morgan brings his famous direct style to the growing numbers of potential mathematics majors who want to see applications along with the theory.
The book is suitable for undergraduates interested in real analysis.
Undergraduate students interested in real analysis and its applications.

Front Cover

Contents

Preface

Part I: Real Numbers and Limits

Chapter 1: Numbers and Logic

Chapter 2: Infinity

Chapter 3: Sequences

Chapter 4: Subsequences

Chapter 5: Functions and Limits

Chapter 6: Composition of Functions

Part II: Topology

Chapter 7: Open and Closed Sets

Chapter 8: Compactness

Chapter 9: Existence of Maximum

Chapter 10: Uniform Continuity

Chapter 11: Connected Sets and the Intermediate Value Theorem

Chapter 12: The Cantor Set and Fractals

Part III: Calculus

Chapter 13: The Derivative and the Mean Value Theorem

Chapter 14: The Riemann Integral

Chapter 15: The Fundamental Theorem of Calculus

Chapter 16: Sequences of Functions

Chapter 17: The Lebesgue Theory

Chapter 18: Infinite Series Σ∞n=1 an

Chapter 19: Absolute Convergence

Chapter 20: Power Series

Chapter 21: The Exponential Function

Chapter 22: Volumes of nBalls and the Gamma Function

Part IV: Fourier Series

Chapter 23: Fourier Series

Chapter 24: Strings and Springs

Chapter 25: Convergence of Fourier Series

Part V: The Calculus of Variations

Chapter 26: Euler’s Equation

Chapter 27: First Integrals and the Brachistochrone Problem

Chapter 28: Geodesics and Great Circles

Chapter 29: Variational Notation, Higher Order Equations

Chapter 30: Harmonic Functions

Chapter 31: Minimal Surfaces

Chapter 32: Hamilton’s Action and Lagrange’s Equations

Chapter 33: Optimal Economic Strategies

Chapter 34: Utility of Consumption

Chapter 35: Riemannian Geometry

Chapter 36: NonEuclidean Geometry

Chapter 37: General Relativity

Partial Solutions toExercises

Greek Letters

Index

Back Cover