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 classic 19th-century textbook that introduces students to the fundamental principles of "differential calculus". First published in 1865, the book carefully explains core concepts such as limits, derivatives, and their applications. Spare emphasizes a structured approach, building on prior knowledge in algebra to make new topics accessible and understandable for learners.
A key feature of the book is its extensive use of "worked examples". Each concept is illustrated through step-by-step problems and practical applications, helping students grasp abstract ideas in a tangible way. Topics such as curve sketching, optimization, and related rates are covered in detail, allowing readers to see how differential calculus can be applied to real-world problems. This methodical approach enhances comprehension and problem-solving skills, making it suitable for both classroom instruction and self-study.
Despite being rooted in 19th-century mathematics, John Spare’s textbook remains relevant for its clarity and pedagogical value. Its focus on foundational concepts, logical structure, and "worked examples" ensures that students can build a strong understanding of differential calculus. For educators and learners seeking a thorough and approachable introduction to calculus, Spare’s work continues to be a trusted resource and reference in mathematical education.
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
was a 19th-century "mathematician" best known for his textbook "Differential Calculus", first published in 1865. His work focused on making "differential calculus" accessible through clear explanations and structured teaching methods, helping students grasp fundamental concepts like limits, derivatives, and optimization. While detailed biographical information about John Spare is limited, his influence endures through his textbooks. His emphasis on clarity, logical structure, and "worked examples" made complex topics understandable.
Read or Downloadable Differential Calculus
Free Differential Calculus Books PDF | Download Study Guides