**AMS/MAA Textbooks**

Volume: 28;
2015;
371 pp;
Hardcover

**Print ISBN: 978-1-93951-206-2
Product Code: TEXT/28**

List Price: $60.00

AMS Member Price: $45.00

MAA Member Price: $45.00

**Electronic ISBN: 978-1-61444-616-3
Product Code: TEXT/28.E**

List Price: $60.00

AMS Member Price: $45.00

MAA Member Price: $45.00

# College Calculus: A One-Term Course for Students With Previous Calculus Experience

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*Michael E. Boardman; Roger B. Nelsen*

MAA Press: An Imprint of the American Mathematical Society

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.

#### Reviews & Endorsements

… 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

# Table of Contents

## College Calculus: A One-Term Course for Students With Previous Calculus Experience

- Cover cov11
- Half title i3
- Copyright ii4
- Title iii5
- Series iv6
- Contents vii9
- Preface xi13
- 0 Preparation for College Calculus 117
- 1 Volume Integrals and Integration by Parts 1127
- 2 Arc Length, Trigonometric Substitution, and Surface Area 3955
- 3 Differential Equations 6581
- 4 Logistic Model, Partial Fractions, Least Squares 91107
- 5 Physical Applications of Integration 115131
- 6 The Hyperbolic Functions 137153
- 7 Numerical Integration 151167
- 8 Parametric Equations and Polar Coordinates 175191
- 9 Improper Integrals, L'Hôpital's Rule, and Probability 211227
- 10 Infinite Series (Part I) 245261
- 10.1 An introduction to series and sequences 245261
- 10.2 Geometric and telescoping series 255271
- 10.3 Monotone sequences 261277
- 10.4 The integral test: series and improper integrals 264280
- 10.5 Comparison tests for positive term series 270286
- 10.6 The alternating series test 273289
- 10.7 Explorations 278294
- 10.8 Acknowledgments 281297

- 11 Infinite Series (Part II) 283299
- 11.1 Absolute and conditional convergence 283299
- 11.2 The ratio and root tests 286302
- 11.3 Convergence tests: a summary and strategy 291307
- 11.4 Power series 292308
- 11.5 The calculus of power series 297313
- 11.6 Taylor and Maclaurin series 305321
- 11.7 Binomial series 313329
- 11.8 Explorations 319335
- 11.9 Acknowledgments 323339

- Appendix A A Description of the AP Calculus AB Course 325341
- Appendix B Useful Formulas from Geometry and Trigonometry 329345
- Appendix C Supplemental Topics in Single Variable Calculus 333349
- Appendix D Supplemental Explorations 345361
- Appendix E Answers to Odd-Numbered Exercises 353369
- Index 367383