College Calculus: A One-Term Course for Students with Previous Calculus Experience is a textbook for students who have successfully experienced an introductory calculus course in high school. College Calculus begins with a brief review of some of the content of the high school calculus course, and proceeds to give students a thorough grounding in the remaining topics in single variable calculus, 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.
The text is ideal as the basis of a course focused on the needs of 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, a course in discrete mathematics, statistics, etc.
0. Preparation for College Calculus
1. Volume Integrals and Integration by Parts
2. Arc Length, Trigonometric Substitution, and Surface Area
3. Differential Equations
4. Logistic Model, Partial Fractions, 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. A Description of the AP Calculus AB Course
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
About the Authors
Michael Boardman and Roger Nelsen both have long affiliations with the AP Calculus program. Nelsen has participated in the annual summer AP readings for 25 years, most of these in AP Calculus (with a stint in AP Statistics). For much of that time, Nelsen 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 eight books including Proof Without Words I, Proofs Without Words II, Math Made Visual, The Calculus Collection, Charming Proofs, and Icons of Mathematics. Boardman’s affiliation with AP Calculus began with the 1994 reading. He was the moderator of the AP Calculus listserv for 10 years, and served four years as Chief Reader for AP Calculus. In this role, he was in charge of all aspects of the scoring of approximately 300,000 exams per year including selecting and supervising 800 readers, finalizing scoring rubrics, overseeing the logistics of the summer reading, and working with College Board personnel to set final cut scores. Boardman also served on the Development Committee for AP Calculus (2007-2011) whose members are responsible for updating the course syllabus, writing the exams, and providing outreach to high school teachers and college faculty. Boardman is currently involved in professional development of AP Calculus teachers, instructing summer and school-year workshops. Boardman serves on several MAA committees including the Committee on the Undergraduate Program in Mathematics.