This is the first modern calculus book to be organized axiomatically and to survey the subject's applicability to science and engineering. A challenging exposition of calculus in the European style, it is an excellent text for a first-year university honors course or for a third-year analysis course. The calculus is built carefully from the axioms with all the standard results deduced from these axioms. The concise construction, by design, provides maximal flexibility for the instructor and allows the student to see the overall flow of the development. At the same time, the book reveals the origins of the calculus in celestial mechanics and number theory.
The book introduces many topics often left to the appendixes in standard calculus textbooks and develops their connections with physics, engineering, and statistics. The author uses applications of derivatives and integrals to show how calculus is applied in these disciplines. Solutions to all exercises (even those involving proofs) are available to instructors upon request, making this book unique among texts in the field.
- Focuses on single variable calculus
- Provides a balance of precision and intuition
- Offers both routine and demanding exercises
"MacCluer's book . . . is calculus 'done right.' And in a mere 162 pages and 1.1 lb! . . . The approach is axiomatic, but the writing style is breezy and inviting. The student will see right away that this is not simply a rehash of material seen in high school--there are some genuinely new ideas here. These include topology, compactness, quantum mechanics, differential equations, and a host of other fascinating topics. . . . This could be an exciting book from which to teach. This is a book that will allow the instructor to build a fascinating course in a variety of different ways. Teaching from this book should be a joy for all."--Steven G. Krantz, UMAP Journal
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