# Byerly’s Elements of the Differential Calculus

Jul 19, 2020

By William E. Byerly, Professor of Mathematics in Harvard University. Judging by the number of editions it was a very popular textbook. Here’s a quick overview in the MAA’s Mathematical Treasures series.

From the 1911 Ginn & Co. textbook catalog:

The distinctive features of this treatise are the rigorous use of the Doctrine of Limits, as a foundation of the subject; the comprehensive treatment of the use of infinitesimals in pure geometry; numerous applications to practical problems in geometry and mechanics.

Links to the Internet Archive’s scans of the 1898 edition:

**Elements of the Differential Calculus**

- Chapter 1: Introduction
- Chapter 2: Differentiation of Algebraic Functions
- Chapter 3: Applications
- Chapter 4: Transcendental Functions
- Chapter 5: Integration
- Chapter 6: Curvature
- Chapter 7: Special Examples and Applications
- Chapter 8: Problems in Mechanics
- Chapter 9: Development in Series
- Chapter 10: Infinitesimals
- Chapter 11: Differentials
- Chapter 12: Functions of More than One Variable
- Chapter 13: Change of Variable
- Chapter 14: Tangent Lines and Planes in Space
- Chapter 15: Development of a Function of Several Variables
- Chapter 16: Maxima and Minima of Functions of Two or More Variables
- Chapter 17: Theory of Plane Curves

**Editions of Elements of the Differential Calculus**

- 1879
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- 1880
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- 1882
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- 1884
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- 1888
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- 1890
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- 1891
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- 1892
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- 1894
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- 1895
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- 1898
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- 1901
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