Calculus for AP®,
2nd Edition

P: Preparation for Calculus
1: Limits and Their Properties
2: Differentiation
3: Applications of Differentiation
4: Integration
5: Differential Equations
6: Applications of Integration
7: Integration Techniques, L’Hopital’s Rule, and Improper Integrals
8: Infinite Series
9: Parametric Equations, Polar Coordinates, and Vectors

Appendices
Appendix A: Proofs of Selected Theorems
Appendix B: Integration Tables
Appendix C: Precalculus Review
C.1 Real Numbers and the Real Number Line
C.2 The Cartesian Plane
C.3 Review of Trigonometric Functions
Appendix D: Algebra Review
Appendix E: Rotation and the General Second-Degree Equation (Online)
Appendix F: Complex Numbers (Online)
Appendix G: Business and Economic Applications (Online)

• Ron Larson

  Dr. Ron Larson is a professor of mathematics at the Pennsylvania State University, where he has taught since 1970. He is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored more than 30 software titles since 1990. Dr. Larson has also written numerous acclaimed textbooks, including the best-selling Calculus Series published by Cengage. He is the recipient of the 2017 William Holmes McGuffey Longevity Award for PRECALCULUS, the 2018 Text and Academic Authors Association TEXTY Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS and the 2017 William Holmes McGuffey Longevity Award for CALCULUS. He also received the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS -- a complete text on CD-ROM that was the first mainstream college textbook to be offered on the internet.

• The AP® Calculus AB and BC mathematical practices are well represented in the examples and exercises. According to the course frameworks for AP® Calculus AB and AP® Calculus BC, the mathematical practices “describe what a student should be able to do while exploring” calculus. To help you in exploration of calculus, we have placed notes and exercises throughout the text highlighting these mathematical practices: Implementing Processes, Connecting Representations, Justification, and Communication and Notation. For more information on these practices (and their corresponding exercises), see page xi.

• Based on market research, feedback from users, and the updates to the course frameworks for AP® Calculus AB and AP® Calculus BC, we have made several changes to the table of contents. We renamed Section 3.7 Linear Approximation and Differentials to better reflect the content covered in the section. The Net Change Theorem has been moved from Section 4.4 The Fundamental Theorem of Calculus to new Section 4.5 The Net Change Theorem. This material was heavily rewritten and two new examples were added. Old Sections 4.5–4.7 are now Sections 4.6–4.8.

• AP® Calculus AB and BC Practice Exams are located after Chapter 9 to help students prepare for the AP® Calculus AB and BC Exams. The practice exams have questions modeled after the types of multiple-choice and free-response questions students will see on the AP® Exam.

• Error Analysis exercises appear in most sections. These exercises present a solution that contains a common error. Students are asked to describe and then correct the error.

• Exploring Concepts exercises appear in each section. These exercises will help you develop a deeper and clearer knowledge of calculus. Work through these exercises to build and strengthen your understanding of calculus concepts.

• Wraparound Teacher’s Edition that includes Paul’s Notes—comprehensive teaching support in every chapter from the coauthor.

• Mathematical Practices for AP® Calculus (MPACs) that are presented in the AP® Curriculum Framework for AP® Calculus AB and BC are represented and clearly labeled in the text, examples, and exercises.

• Calculus AP® Exam Preparation Questions are modeled after the AP® exam and appear at both the end of section exercises and chapter.

• Insights are AP® specific and appear throughout the book to offer important information about material commonly appearing on the AP® Exam.

• Performance Tasks appear at the end of each chapter asking students to demonstrate their understanding of chapter content.

• Algebra Review appears throughout each chapter and offers support at point of use.

• Side-By-Side Examples offer solutions from multiple perspectives—algebraically, graphically, and numerically, allowing students to see a problem more conceptually and learn how different methods yield the same result.

• LarsonCalculusforAP.com is a free support website that has been updated with videos explaining mathematical concepts or proofs. Explore examples, view three-dimensional graphs, review sample scoring for free-response questions, and much more.

• The website CalcView.com contains video solutions of selected exercises. Watch instructors progress step-by-step through solutions, providing guidance to help you solve the exercises. The CalcView mobile app is available for free at the Apple® App Store® or Google Play™ store. Use the embedded QR Code reader to scan on-page codes to launch videos.

• The website CalcChat.com provides free step-by-step solutions to all odd-numbered section and review exercises. Also, students can chat with a tutor, at no charge, during the hours posted at the site. The CalcChat mobile app is available for free at the Apple® App Store® or Google Play™ store.

Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

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