College Calculus
A One-Term Course for Students with Previous Calculus Experience

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.

Preface; 0. Preparation for college calculus; 1. Volume integrals and integration by parts; 2. Arc length, trigonometric substitution, and surface area; 3. Differential equations; 4. The logistic model, partial fractions, and least squares; 5. Physical applications of integration; 6. The hyperbolic functions; 7. Numerical integration; 8. Parametric equations and polar coordinates; 9. Improper integrals, L'Hôpital's rule, and probability; 10. Infinite series (part I); 11. Infinite series (part II); Appendix A. Topic outline for AP calculus AB; Appendix B. Useful formulas from geometry and trigonometry; Appendix C. Supplemental topics in single variable calculus; Appendix D. Supplemental explorations; Appendix E. Answers to odd-numbered exercises; Index.

Michael Boardman received his BS and MS in mathematics from Western Washington University and his PhD in mathematics from the University of Oregon in 1992. After receiving his PhD, Boardman taught at Lake Forest College. Since 1995, he has been at Pacific University. Boardman's long affiliation with AP Calculus began with the 1994 reading. He was the moderator of the AP Calculus listserv for ten years, and served as Chief Reader for the AP Calculus program during 2008–11. In this role, he oversaw all aspects of scoring what was then approximately 300,000 exams per year, supervising 800 readers, finalizing scoring rubrics, and overseeing the logistics of the two-week summer reading. Boardman served on the Development Committee for AP Calculus for 5 years and currently provides professional development for AP Calculus teachers, instructing summer and school-year workshops. Boardman serves on several MAA committees including the Committee on the Undergraduate Program in Mathematics.
Roger Nelsen received his BA in mathematics from DePauw University in 1964 and his PhD in mathematics from Duke University in 1969. He taught mathematics and statistics at Lewis and Clark College for forty years before his retirement in 2009. Nelsen has had a long affiliation with the AP Calculus program. He has participated in the annual summer AP readings for over twenty-five years, most of these in AP Calculus, with a stint in AP Statistics. For much of that time, he served as a Table Leader, and more recently as a member of a question team, responsible for working out the details of scoring a particular free-response question. Nelsen is the author or co-author of seven MAA books: Proofs without Words, Proofs without Words II, Math Made Visual, When Less Is More, The Calculus Collection, Charming Proofs and Icons of Mathematics.