Differential Calculus by John Spare
Differential Calculus - Table of Contents
- 1. Elementary Principles
- 2. Definitions Relating to Functions
- 3. The Degrees of an Equation, First and Second Degree
- 4. Increase of the Value of Functions, Decrease of the Value of Functions, Stationary Values of Them
- 5. The Binomial Series, Solutions of Problems by Inequations
- 6. Differential of Variable, Differential of Function
- 7. First Differential Coefficient
- 8. Use of First Differential Coefficient
- 9. Successive Differentiation, Second, Third Differentials
- 10. Taylor's Theorem
- 11. Theory of Maxima and Minima
- 12. Problem Furnishing Explicit Functions of One Variable, For Determining Their Maxima and Minima
- 13. Complete History of Functions
- 14. Principles and Problems Relating to Prjected Bodies
- 15. The System of Symbols for Functions, An Implicit Function of a Single Independent Variable and its Differentiation
- 16. Problems Which May Furnish Implicit Functions of One Varaible and Cases of Their Maxima and Minima
- 17. Problems of Two Independent Varaibles, Their Differentiation and Their Maxima and Minima
- 18. Problems Relating to Functions of Two Independent Varaibles and Cases of Their Maxima and Minima
- 19. Demonstration of the General Form of the Development of f(x+h), and of the Differentiation of Certain Functions
- 20. Maclaurin's Theorem and Its Application
- 21. Determination of the Value of Vanishing Fractions
- 22. Exceptional Principle Relating to Taylor's Theorem
- 23. Nature of Lograithms and Exponential Quantities
- 24. Differentiation and Development of Logarithmic and Exponential Functions
- 25. Examples of the Differentiation and Development of Logarithmic Functions
- 26. Examples of the Differentiation and Analysis of Exponential Functions, Including Examples from Compound Interest and Increase of Population
- 27. Differentiation of Circular Functions
- 28. Geometric Illustrations of the Values of Functions and the Corresponding Values of their Variables also of the Value of Differential Coefficients, Maxima and Minima etc.
What You Will Learn in Differential Calculus
Differential Calculus by John Spare is a landmark 19th-century mathematical work written to clarify the fundamental mechanics of rates of change and fluxions for advanced students. Combining clear theoretical exposition with systematic problem-solving steps, this classical text serves as a valuable resource for differential calculus study practice.
The volume thoroughly explores the origin of differentials, expansion of algebraic and transcendental functions, successive differentiation, maxima and minima, and tangents to curves. By pairing logical mathematical proofs with clear step-by-step demonstrations, Spare enables readers to apply fundamental calculus differentiation rules with total clarity and analytical confidence.
Revered by historians and mathematicians for its lucid pedagogy and unique historical perspective, this timeless volume remains an excellent reference for self-directed study and research. Spare’s methodical exposition equips learners with the analytical tools required for mastering single variable derivative applications across mathematical analysis.
Book Details & Specifications
Title:
Differential Calculus by John Spare
Publisher:
Bradley, Dayton and Company, Boston
Year:
1865
Pages:
283
Type:
PDF
Language:
English
ISBN-10 #:
3375053975
ISBN-13 #:
978-3375053970
License:
Public Domain Work
Amazon:
Amazon
About the Author: John Spare
The author John Spare
, M.D. (1816–1901) was an American physician, scholar, and avid mathematician who graduated from Amherst College and Harvard Medical School. Alongside his medical practice in Massachusetts, Spare maintained a lifelong passion for higher mathematics and classical pedagogy.
Driven by a desire to simplify complex analytical ideas for students, Spare authored comprehensive treatise work on differential calculus. His classical writings stand as remarkable contributions to 19th-century American mathematical literature and remain respected historical calculus educational reference materials.
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