| Softcover ISBN: | 978-1-4704-6501-8 |
| Product Code: | REALAPP.S |
| List Price: | $55.00 |
| MAA Member Price: | $49.50 |
| AMS Member Price: | $44.00 |
| eBook ISBN: | 978-1-4704-1214-2 |
| Product Code: | REALAPP.E |
| List Price: | $49.00 |
| MAA Member Price: | $44.10 |
| AMS Member Price: | $39.20 |
| Softcover ISBN: | 978-1-4704-6501-8 |
| eBook: ISBN: | 978-1-4704-1214-2 |
| 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: | 978-1-4704-6501-8 |
| Product Code: | REALAPP.S |
| List Price: | $55.00 |
| MAA Member Price: | $49.50 |
| AMS Member Price: | $44.00 |
| eBook ISBN: | 978-1-4704-1214-2 |
| Product Code: | REALAPP.E |
| List Price: | $49.00 |
| MAA Member Price: | $44.10 |
| AMS Member Price: | $39.20 |
| Softcover ISBN: | 978-1-4704-6501-8 |
| eBook ISBN: | 978-1-4704-1214-2 |
| 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 |
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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
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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 n-Balls and the Gamma Function
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Part IV: Fourier Series
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Chapter 23: Fourier Series
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Chapter 24: Strings and Springs
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Chapter 25: Convergence of Fourier Series
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Part V: The Calculus of Variations
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Chapter 26: Euler’s Equation
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Chapter 27: First Integrals and the Brachistochrone Problem
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Chapter 28: Geodesics and Great Circles
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Chapter 29: Variational Notation, Higher Order Equations
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Chapter 30: Harmonic Functions
-
Chapter 31: Minimal Surfaces
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Chapter 32: Hamilton’s Action and Lagrange’s Equations
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Chapter 33: Optimal Economic Strategies
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Chapter 34: Utility of Consumption
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Chapter 35: Riemannian Geometry
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Chapter 36: NonEuclidean Geometry
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Chapter 37: General Relativity
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Partial Solutions toExercises
-
Greek Letters
-
Index
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Back Cover
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Additional Material
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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 n-Balls 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
