College Calculus: A One-Term Course for Students with Previous Calculus Experience (Mathematical Association of America Textbooks) - Tapa dura

In College Calculus: A One-Term Course for Students with Previous Calculus Experience, Michael E. Boardman and Roger B. Nelsen have written a solid text for the serious calculus student. It is intended for the students who had a successful experience with an introduction to calculus in high school or have scored a 4 or a 5 on the AP Exam. The text begins with a review of some of the topics found in an AP calculus course and provides readers with a preview of what to expect in their future mathematics courses. Chapter 0 is a preparation for college calculus, but it very brief, with a review of limits, continuity, derivatives, and integration. Chapters 1-11 contain material normally found in Calculus II, with topics from volumes of surfaces of revolution to infinite series. Boardman and Nelsen have done a great job putting this text together, especially in the chapters on infinite series. They have split this large topic into two chapters, which is much better for the student to absorb. Most calculus texts will have all of the sequences and series topics along with all of the tests for convergence and divergence along Taylor and Maclaurin series in one big chapter. It has been my experience, by the time I have finished teaching sequences and series, students are burned out. With this split up, students will be able to study these concepts in smaller chunks. As with the other chapter exercises, the problems progress from easy to difficult. Chapters 10 and 11 have this same set-up with questions that can be used as project or group research projects. Among my favorites is Gabriel's wedding cake found on page 270. Here students must show Gabriel's wedding cake is a cake that one can eat but cannot frost. In other words, like Gabriel's horn, it has a finite volume but infinite surface area. At the end of the book, there are five appendices, the first of which provides the instructor with a description of the AP Calculus AB Course. This serves as an information page so that instructors have a better understanding of the type of students they will have in their classroom. My only suggestion would be to add color to the pictures, charts, and graphs. Simply put, this is a well-written text. Both Boardman and Nelsen have shown their knowledge and years of experience. I see this text being used in many different ways. Instructors can assign this text as summer reading as they progress to multivariable calculus, linear algebra, or ordinary and partial differential equations. It can also be used as a resource for tutors while tutoring or as supplementary or primary reading for Calculus II. It can also be used for the instructor to use for in-class examples or test questions. No matter how used, the student is sure to gain the knowledge of Calculus II and have a leg up over other students. I highly recommend this book."" - Peter Olszewski, MAA Reviews

For students who have completed an introductory calculus course in high school, this textbook provides a thorough grounding in many subsequent single variable calculus topics. Beginning with a review of some high school calculus content, it proceeds to more advanced material including integration techniques, applications of the definite integral, separable and linear differential equations, hyperbolic functions, parametric equations and polar coordinates, L'Hôpital's rule and improper integrals, continuous probability models, and infinite series. Each chapter concludes with several 'Explorations', extended discovery investigations to supplement that chapter's material and enhance the learning experience. The text is ideal as the basis of a course for prospective majors in the STEM disciplines (science, technology, engineering, and mathematics). A one-term course based on this text provides students with a solid foundation in single variable calculus and prepares them for the next course in college-level mathematics, be it multivariable calculus, linear algebra, discrete mathematics or statistics.