Single variable calculus : concepts and contexts

Abstract

When the first edition of this book appeared twelve years ago, a heated debate about calculus reform was taking place. Such issues as the use of technology, the relevance of rigor, and the role of discovery versus that of drill were causing deep splits in mathematics departments. Since then the rhetoric has calmed down somewhat as reformers and traditionalists have realized that they have a common goal: to enable students to understand and appreciate calculus. The first three editions were intended to be a synthesis of reform and traditional approaches to calculus instruction. In this fourth edition I continue to follow that path by emphasizing conceptual understanding through visual, verbal, numerical, and algebraic approaches. I aim to convey to the student both the practical power of calculus and the intrinsic beauty of the subject. The principal way in which this book differs from my more traditional calculus textbooks is that it is more streamlined. For instance, there is no complete chapter on techniques of integration I don’t prove as many theorems (see the discussion on rigor on page xv) and the material on transcendental functions and on parametric equations is interwoven throughout the book instead of being treated in separate chapters. Instructors who prefer fuller coverage of traditional calculus topics should look at my books Calculus, Sixth Edition, and Calculus: Early Transcendentals, Sixth Edition.