Elements of Differential and Integral Calculus (1911) is a comprehensive and foundational text that serves as a fundamental introduction to the subject matter of calculus. Authored by renowned mathematician William Anthony Granville, this book was first published over a century ago and has since remained a timeless classic in the field of calculus.
The book is structured in a way that builds a strong foundation for students who are new to calculus, and it is also an excellent resource for those seeking to brush up on their calculus knowledge. The text covers the basic principles of calculus, including limits, differentiation, integration, and their applications in real-world scenarios.
The chapters on limits and continuity are especially helpful for students just beginning to learn calculus. Granville provides clear explanations and examples, making it easy to understand the fundamental concepts. He then moves on to derivatives and their applications in physics, engineering, and other sciences. The author also covers the chain rule, product rule, and quotient rule, making sure that the reader has a strong grasp of these essential concepts.
In the second part of the book, Granville covers integrals and their applications, including finding areas, volumes, and arc lengths. The author provides plenty of examples and exercises to help students practice the techniques they have learned. This section of the book is particularly useful for students in engineering, physics, and other scientific fields where the calculation of integrals is essential.
The final chapter of the book deals with infinite series, which is an essential concept in calculus. The author provides a comprehensive overview of the topic, from the basics of sequences to the convergence of series. Granville’s clear explanations and examples make this often daunting subject easy to understand.
In summary, Elements of Differential and Integral Calculus (1911) is an excellent resource for anyone interested in learning calculus. It is a comprehensive and foundational text that covers all of the essential concepts, providing readers with a solid foundation to build upon. The book is easy to follow, with clear explanations and plenty of examples and exercises to help readers practice their skills. It is a must-read for students and professionals alike who are looking to master the principles of calculus.