Calculus and Analytic Geometry

Gillett's love of mathematics and his love of teaching shine forth in this book. His narrative is conversational and easy to follow. He motivates new ideas with both historical context and conceptual considerations. He helps the reader to see math as a living and historical process, rather than a fixed body of facts. His style--for instance, asking questions at key junctures to prod the reader's own thinking--invites the reader to join in the adventure of discovery. He opens every chapter with insightful quotations on math, the universe, and everything from a broad constellation of luminaries--from Newton, to Whitehaed, to Einstein, to Twain, to Plato, to Whitehead... The proofs are excellent and easy to follow. More technical or difficult ones are placed at the end of the section so as to not interrupt the flow of ideas. The illustration are appropriate and ample. Exercises are a good mix of computations and theory. My favorites are the multipart puzzles that he guides the reader to explore and, with effort, conquer. I still recall the proof, using double integrals, that int(e^(-x^2))[0 to infty] = sqrt(pi)/2... I still have my copy from 20 years ago when I first learned calculus! The book is that good!