Differential and Integral Calculus by George Osborne
Differential and Integral Calculus - Table of Contents
Part-I DIFFERENTIAL CALCULUS
- 1. Functions, Variables and Constants
- 2. Limit. Increment. Derivative
- 3. Differentiation
- 4. Successive Differentiation, Leibnitz's Theorem
- 5. Differentials. Infinitesimals
- 6. Implicit Functions
- 7. Series. Power Series
- 8. Expansion of Functions
- 9. Indeterminate Forms
- 10. Maxima and Minima of Functions of One Independent Variable
- 11. Partial Differentiation
- 12. Change of the Variables in Derivatives
- 13. Maxima and Minima of Functions of Two or More Variables
- 14. Curves for Reference
- 15. Direction or Curves. Tangents and Normals
- 16. Direction op Curvature. Points of Inflexion
- 17. Curvature. Radius of Curvature. Evolute and Involute
- 18. Order of Contact. Osculating Circle
- 19. Envelopes, Series of Curves
Part-II INTEGRAL CALCULUS
- 20. Integration of Standard Forms
- 21. Simple Applications of Integration. Constant of Integration
- 22. Integration of Rational Fractions
- 23. Integration of Irrational Functions
- 24. Trigonometric Forms readily Integrable
- 25. Integration by Parts. Reduction Formulae
- 26. Integration by Substitution
- 27. Integration as a Summation. Definite Integrals
- 28. Application of Integration to Plane Curves. Application to Certain Volumes
- 29. Successive Integration, Definite Double Integral. Variable Limits. Triple Integrals
- 30. Applications of Double Integration
- 31. Surface, Volume, and Moment of Inertia of Ant Solid
- 32. Centre of Gravity. Pressure of Eldids. Eorce of Attraction
- 33. Integrals for Reference
What You Will Learn in Differential and Integral Calculus
Differential and Integral Calculus by George A. Osborne is an influential 19th-century mathematical manual engineered to deliver a balanced, practical foundation in real analysis for colleges and scientific schools. Designed for analytical clarity, this masterwork serves as an outstanding reference for differential integral calculus problem practice.
The text systematically explores derivatives, rates of change, partial differentiation, expansion of series, definite integrals, and geometric applications to areas and volumes. By pairing clear theoretical demonstrations with rigorous drill problems, Osborne enables learners to apply fundamental calculus differentiation and integration rules with complete precision and confidence.
Praised for its logical organization and accessible pedagogical style, this timeless volume remains an excellent asset for coursework revision and self-directed study. Osborne’s systematic exposition arms students with the exact analytical tools required for mastering single and multivariable derivative applications across technical subjects.
Book Details & Specifications
Title:
Differential and Integral Calculus by George Osborne
Publisher:
Boston, D. C. Heath
Year:
1906
Pages:
408
Type:
PDF
Language:
English
ISBN-10 #:
1112347585
ISBN-13 #:
978-1112347580
License:
Public Domain Work
Amazon:
Amazon
About the Author: George Abbott Osborne
The author George Abbott Osborne
(1839–1927) was a distinguished American mathematician and Walker Professor of Mathematics at the Massachusetts Institute of Technology (MIT). Serving MIT for over four decades, he was instrumental in shaping early American engineering and scientific mathematics instruction.
Known for his devotion to clear teaching and rigorous textbook development, Professor Osborne published foundational manuals in calculus and algebra. His classic works remain benchmark references for educators building timeless university level calculus reference materials.
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