Differential and Integral Calculus: With Examples and Applications by George A Osborne

About this book :-
"Differential and Integral Calculus: With Examples and Applications" by George A. Osborne is a classic calculus textbook that has guided students for over a century. Written for learners of average mathematical ability, it carefully introduces core concepts of "differential and integral calculus", starting with limits and derivatives, then progressing to applications like maxima, minima, and curvature. Osborne’s clear, step-by-step explanations make challenging topics accessible and provide a solid foundation for further study. The book emphasizes "practical applications" in physics, engineering, and real-world problem solving. Each chapter includes numerous examples and exercises, helping students apply theory to concrete situations. Osborne’s approach ensures that readers not only understand the mathematical techniques but also learn to use them effectively, bridging the gap between abstract calculus concepts and everyday applications. Though written in the late 19th century, the text remains relevant for understanding the evolution of calculus education. Its notations may feel old-fashioned, but the principles and problem-solving strategies are timeless. Today, Osborne’s work is freely available online, offering both historical insight and a comprehensive introduction to calculus. For anyone studying mathematics or exploring classic textbooks, this work is an invaluable resource in the field of "calculus".

Book Detail :-
Title: Differential and Integral Calculus: With Examples and Applications by George A 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 Author :-
The author George A. Osborne (1839–1927) was a prominent American "mathematician" and educator, best known for his influential work in "calculus education". He served as a professor at the Massachusetts Institute of Technology (MIT), shaping the early mathematics curriculum and mentoring generations of students. Osborne aimed to make complex mathematical concepts accessible, emphasizing clarity and practical understanding. He authored "Differential and Integral Calculus: With Examples and Applications", a classic textbook that combines theory with real-world applications. Osborne’s approach to teaching calculus made it approachable for students of varying skill levels and left a lasting legacy in the field of mathematical education.

Book 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

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