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The Calculus Gallery
Masterpieces from Newton to Lebesgue
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William Dunham
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With contributions by:
William Dunham
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Preface by:
William Dunham
Language:
English
Published/Copyright:
2018
About this book
More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway to higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth. Now with a new preface by the author, this book documents the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching—a story of genius triumphing over some of the toughest, subtlest problems imaginable. In touring The Calculus Gallery, we can see how it all came to be.
Author / Editor information
William Dunham is a Research Associate in Mathematics at Bryn Mawr College. He is the author of Journey Through Genius: The Great Theorems of Mathematics, The Mathematical Universe, and Euler: The Master of Us All, and is a co-editor (along with Jerry Alexanderson and Don Albers) of The G.H. Hardy Reader. He received the Mathematical Association of America's George Polya, Trevor Evans, and Lester R. Ford awards, as well as its Beckenbach Prize for expository writing.
Reviews
"This is a book that should be part of the personal library of any mathematician."---Mark Hunacek, Mathematical Gazette
Topics
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Frontmatter
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Contents
vii -
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Illustrations
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Acknowledgments
xiii -
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Preface to the Princeton Science Library Edition
xv -
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INTRODUCTION
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CHAPTER 1. Newton
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CHAPTER 2. Leibniz
20 -
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CHAPTER 3. The Bernoullis
35 -
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CHAPTER 4. Euler
52 -
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CHAPTER 5. First Interlude
69 -
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CHAPTER 6. Cauchy
76 -
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CHAPTER 7. Riemann
96 -
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CHAPTER 8. Liouville
116 -
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CHAPTER 9. Weierstrass
128 -
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CHAPTER 10. Second Interlude
149 -
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CHAPTER 11. Cantor
158 -
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CHAPTER 12. Volterra
170 -
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CHAPTER 13. Baire
183 -
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CHAPTER 14. Lebesgue
200 -
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Afterword
220 -
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Notes
223 -
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Index
233
Publishing information
Pages and Images/Illustrations in book
eBook published on:
January 14, 2019
eBook ISBN:
9780691184548
Pages and Images/Illustrations in book
eBook ISBN:
9780691184548
Keywords for this book
Mathematician; Theorem; Mathematics; Series (mathematics); Bernhard Riemann; Continuous function; Pointwise; Summation; Riemann integral; Real number; Infinitesimal; Natural number; Division by zero; Differentiable function; Counterexample; Augustin-Louis Cauchy; Interval (mathematics); Coefficient; Karl Weierstrass; Polynomial; Set theory; Nowhere continuous function; Quantity; Algebraic number; Equation; Transcendental number; Infinity; Dense set; Uniform convergence; Geometry; Continuous function (set theory); Infimum and supremum; Georg Cantor; Harmonic series (mathematics); Henri Lebesgue; Mathematical analysis; Derivative; Differential calculus; Tangent; Q.E.D.; Integer; Theory; Scientific notation; Existential quantification; Measurable function; Princeton University Press; Vito Volterra; Geometric progression; Real analysis; Geometric series; Fourier series; Intermediate value theorem; Westmont College; Bounded function; Mean value theorem; Rational number; Binomial theorem; Subset; Contradiction; Absolute value; Antiderivative; Sign (mathematics); Unit interval; Baire category theorem; Fundamental theorem; Lebesgue integration; Upper and lower bounds; Notation; Diagram (category theory); Countable set
Audience(s) for this book
For an expert adult audience, including professional development and academic research
