Calculus in Context: Background, Basics, and Applications

"The depth of detail in each application [offered by Calculus in Context] provides an excellent structure for guiding students through the 'why should we care' moments that every calculus class experiences."
(Mathematical Association of America)

"Recommended."
(Choice)

"Hahn's book is the perfect choice for college and university teachers who want to teach calculus with reference to its origins and applications."
(Zentralblatt Math)

"Very well written in an engaging and enthusiastic style: it is very suitable for first year students, is perhaps not too demanding for students about to enter university, and it is particularly useful to those with more than a passing interest in astronomy. There is plenty to learn for the reader,and the massive text is also a good reference book on calculus. This labour of love from the author more than satisfies the high hopes for a good calculus book... and I highly recommend it."
(Peter Shiu Mathematical Gazette)

The following review appeared in the October 2017 issue of Choice Reviews, Association of College and Research Libraries..
There is no question that this book addresses the age-old mantra "What is this good for?" Part 1 starts off with ancient Greek astronomy, a motivating force for the development of early mathematics. Anchored to the historical underpinnings of these investigations, Hahn (Univ. of Notre Dame) presents the necessary geometry, trigonometry, and algebra to explore these problems. The historical thread continues through the next three chapters, ultimately leading to separate chapters on the calculus of Leibniz and Newton. Problem sets include applied investigations and pure mathematical considerations throughout. Part 2 introduces definitions and procedures found in single variable calculus, but even here the presentation is not traditional. The author avoids focusing on content and techniques that are rarely used in applied settings. Instead he provides succinct coverage of necessary calculus principles, leading to additional problems and projects drawn from those physics settings that directly connect to these mathematical concepts. In the end, a brief presentation of first- and second-order differential equations supports the final applications including, appropriately, astronomical considerations, which nicely counterbalance the start of the book. Overall, this text effectively lives up to its promise of "calculus in context."
N. W. Schillow, Lehigh Carbon Community College
Summing Up: Recommended. Lower-division undergraduates.

Zentralblatt MATH 1379 | 1
Calculus in context is the newest book of Alexander J. Hahn who has already published (Basic Calculus. From Archimedes to Newton to its Role in Science. New York, NY: Springer, 1998; Zbl 913.00007). This work being out of print, the new book can be understood as an expanded reissue which profits from nearly 20 years of additional teaching experience. The first part of the book comprises four pre-analytical chapters on topics such as geometry, trigonometry and astronomy in Ancient Greece, the astronomy of the Renaissance and Descartes' coordinate geometry, as well as two historical chapters on the differential calculus of Leibniz and Newton. The second part of the book gives a condensed but robust introduction to contemporary differential and integral calculus, differential equations and polar calculus, devoting as much space to applications as is devoted to theory. In the course of this, Hahn excels in linking the mathematical knowledge and skills needed for further studies in analysis to typical applications, whose presentation is catching and demanding. The 692-pages book also includes over 100 pages of problems and projects which provide a rich source for practice and further study. I completely support Hahn's position that the book can be used both as a traditional introduction into the mathematical aspects of calculus with occasional references to its history and applications, and as a genetic approach towards calculus which begins with its history and applications. Given the range of mathematical topics which Hahn addresses in the first chapters, I would even argue that Hahn's book can be used as a more general introduction to academic mathematics, including, e.g., elementary geometry. One thing that I missed, however, was explicit information on how to understand and establish a mathematical proof. Given that proving is one of the most diffcult aspects for novice students of academical mathematics, a more careful introduction to the art of proving would have been beneficial. For that purpose, Hahn's discussion of Euclid's elements and basic proofs in the first chapter might have marked just the perfect spot.
Hahn's book is the perfect choice for college and university teachers who want to teach calculus with reference to its origins and applications. The book can easily be used to prepare lessons. The problems provided in the book are wonderful to facilitate practice and discussion. However, the text is also understandable to the interested student, making the book a good choice for seminar work as well. Hahn himself reports to have used the resources for teaching by having teams of students work on the understanding and presentation of an applied topic of calculus on the basis of the book. Whatever style of teaching is preferred, Hahn's book should de nitely have its place on the bookshelf.
David Kollosche (Berlin)