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1. Introduction 2. Differentiation of Algebraic Functions 3. Applications (Tangents and Normals) 4. Transcendental Functions 5. Integration 6. Curvature 7. The Cycloid 8. Problems in Mechanics 9. Development of Series 10. Infinitesimals 11. Differentials 12. Functions of More Than One Variable (Partial Derivatives) 13. Change of Variables 14. Tangent Lines and Planes in Space 15. Development of a Function of Several Variables 16. Maxima and Minima of Functions of Two or More Variables 17. The Theory of Plane Curves
Elements of the Differential Calculus with Examples and Applications by William Elwood Byerly is an influential late 19th-century educational manual written to make higher analysis accessible to university undergraduates. Designed for rigor and clarity, this foundational textbook serves as an exceptional guide for differential calculus problem solving practice. The volume systematically covers limits, rate of change, algebraic differentiation, transcendental functions, series expansion, partial differentiation, and geometric applications. By combining strict analytical demonstrations with step-by-step practical examples, Byerly enables readers to execute fundamental calculus differentiation rules with total clarity and confidence. Revered by educators for its direct instructional layout and extensive exercise sets, this historic Harvard text remains a highly valuable asset for independent study. Byerly’s structured methodology arms students with the logical framework needed for mastering classical single variable derivative applications across physical sciences.
Title: Elements of Differential Calculus by William Byerly Publisher: Ginn & Co. Year: 1879 Pages: 282 Type: PDF Language: English ISBN-10 #: 333781297X ISBN-13 #: 978-3337812973 License: Public Domain Work Amazon: Amazon
The author William Elwood Byerly (1849–1935) was a distinguished American mathematician and the Perkins Professor of Mathematics at Harvard University. He was notably the first recipient of a Ph.D. from Harvard University in 1873 and played a foundational role in establishing Radcliffe College for women. Famous for his exceptionally clear lecturing style and practical pedagogical approach, Dr. Byerly authored seminal textbooks in calculus, Fourier series, and spherical harmonics. His works remain landmark references for educators seeking rigorous classical mathematics study materials.
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