Differential and Integral Calculus by De Morgan Augustus
Differential and Integral Calculus - Table of Contents
1. On the Processes of Direct Differentiation
2. On the General Theory of Functional Increments and Differentiation
3. On Algebraical Development
4. Calculus of Finite Differences
5. On Implicit Differentiation
6. Meaning of, and Processes in, Integration
7. Trigonometrical Analysis
8. On the Meaning of Differential Coefficients, and on the First Principles of the Application of the Science to Geometry and Mechanics
9. On the Connexion of Differentiations of Different Kinds
10. On Singular Values
11. On Differential Equations
12. Further Applications to Algebra
13. Miscellaneous Examples and Developments
14. Application to Geometry of Two Dimensions
15. Application to Geometry of Three Dimensions
16. On the Calculus of Variations
17. Application to Mechanics
18. On Interpolation and Summation
19. On the Transformation of Divergent Developments
20. On Definite Integrals
21. On Differential Equations and Equations of Differences
What You Will Learn in Differential and Integral Calculus
"Differential and Integral Calculus" by "Augustus De Morgan" is a foundational guide to understanding "differential calculus". The book introduces key concepts such as derivatives, limits, and rates of change in a structured and clear manner. De Morgan emphasizes logical reasoning, step-by-step explanations, and thorough proofs, helping students build a strong theoretical foundation while developing analytical and problem-solving skills.
Beyond differentiation, the text extensively covers "integral calculus", showing how integrals are used to calculate areas, solve equations, and model real-world phenomena. Each chapter contains worked examples and exercises designed to reinforce concepts and improve computational skills. By combining theory with practical applications, De Morgan enables readers to connect calculus principles to science, engineering, and applied mathematics.
The treatise also serves as an essential resource for "mathematical analysis", linking calculus fundamentals to broader analytical reasoning. Ideal for students, educators, and self-learners, De Morgan’s work provides a structured approach to mastering calculus. Its clarity, examples, and exercises make complex topics approachable, ensuring readers gain both conceptual understanding and hands-on experience in differential and integral calculus, making it a lasting reference in mathematics education.
Book Details & Specifications
Title:
Differential and Integral Calculus by De Morgan Augustus
Publisher:
R. Baldwin
Year:
1842
Pages:
882
Type:
PDF
Language:
English
ISBN-10 #:
1293863807
ISBN-13 #:
978-1293863800
License:
Public Domain Work
Amazon:
Amazon
About the Author: De Morgan Augustus
The author
De Morgan Augustus
was a British "mathematician", who studied at Trinity College, Cambridge, developing a strong foundation in "mathematical analysis" and logic. De Morgan became the first Professor of Mathematics at University College London, teaching for many years and influencing generations of students. He authored "Differential and Integral Calculus", focusing on "differential calculus" and "integral calculus", with clear explanations and worked examples. His contributions to mathematics education helped bridge theory and practical applications, making advanced calculus concepts accessible to students and scholars.
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