Single Variable Calculus

Built from the ground up to meet the needs of today's calculus learners,Single Variable Calculus was the first book to pair a complete calculus syllabus with the best elements of reform--like extensive verbalization and strong geometric visualization. The Third Edition of this groundbreaking book has been crafted and honed, making itthe book of choice for those seeking the best of both worlds. Numerous chapters offer an exciting choice of problem sets and include topics such as functions and graphs, limits and continuity, differentiation, additional applications of the derivative, integration, additional applications of the integral, methods of integration, infinite series, vectors in the plane and in space, and vector-valued functions. For individuals in fields related to engineering, science, or mathematics.

This text was developed to blend the best aspects of calculus reform with the reasonable goals and methodology of traditional calculus. It achieves this middle ground by providing sound development, stimulating problems, and well-developed pedagogy within a framework of a traditional structure. "Think, then do," is a fair summary of our approach. New to this Edition The acceptance and response from our first two editions has been most gratifying. For the third edition, we wanted to take a good book and make it even better. If you are familiar with the previous editions, the first thing you will notice is that we have added a new coauthor, Monty J. Strauss. His added expertise, and his attention to accuracy and detail, as well as his many years of experience teaching calculus, have added a new dimension to our exposition. Here is what is new in the third edition: Organization In this edition we introducee x and lnxin Chapter 2 after we have defined the notion of a limit. This is beneficial because it allows the numbereto be properly defined using limits. We also assume a knowledge of the conic sections and their graphs. A freeStudent Mathematics Handbookis available that provides review and reference material on these transcendental functions. l'Hopital's Rule is now covered earlier in Chapter 4. This placement allows instructors to explore more interesting applications like curve sketching. A new section covering applications to business, economics, and the life sciences has been added to Chapter 6 on Applications of the Integral. This new material is designed to help students see how calculus relates to and is used in other disciplines. The chapter on polar coordinates and parametric forms has been distributed to other chapters in the book. The polar coordinate system and graphing in polar forms is in Chapter 6 in the context of the integration topic of finding areas. Parametric representation of curves now appears in the book where it is first needed, in Chapter 9. Modeling continues as a major theme in this edition. Modeling is now introduced in Section 3.4, and then appears in almost every section of the book. These applications are designated MODELING PROBLEMS. Some authors use the words "Modeling Problem" to refer to any applied problem. In the third edition ofCalculus,we make a distinction betweenmodeling problemsandapplication problemsby defining a modeling problem as follows. Amodeling problemis a problem that requires that the reader make some assumptions about the real world in order to derive or come up with the necessary mathematical formula or mathematical information to answer the question. These problems also include real-world examples of modeling by citing the source of the book or journal that shows the modeling process. Problem Sets We have added a new major category of problems, calledcounterexample problem.Acounterexampleis an example that disproves a proposition or theorem, and in mathematics we are often faced with a proposition that is true or false, and our task is to prove the proposition true or to find a counterexample to disprove the proposition. In the third edition ofCalculus,we attempt to build the student's agility with this type of situation to mean that the student must either find justification that the proposition is true or else find a counterexample. We believe this new form of problem to be important for preparing the student for future work in not only advanced mathematics courses, but also for analytically oriented courses. Exploration Problemsexplore concepts which may prove true or false and provide opportunities for innovative thinking. Interpretation Problemsrequire exposition that requires a line of thinking that is not directly covered in the textbook. S