Calculus, 2nd Edition, AP Edition © 2018
William Briggs | Lyle Cochran | Bernard Gillett
William Briggs and Lyle Cochran have developed a unique program tailored for AP Calculus teachers and students. The program begins with a captivating and succinct narrative that stimulates students' intuition and geometric understanding. Throughout each chapter, practical examples, relatable analogies, and contemporary applications are presented, making calculus understandable and relatable. This program not only aids students in reaching their AP objectives but also establishes a solid groundwork for future college-level studies.
- This program is designed to align directly with the AP Curriculum Framework, ensuring that students are well-prepared for the AB or BC exam.
- An innovative and acclaimed eTextbook is included, featuring over 400 interactive figures that are directly taken from the book. These figures can be accessed through MyMathLab® for School, enabling teachers to effectively illustrate crucial concepts in the classroom.
- Margin notes throughout the book encourage students to actively participate in their learning by reading with a pencil in hand, promoting a deeper understanding of the content.
- Each chapter ends with comprehensive exercise sets that gradually build on previous knowledge and a dedicated section of AP practice exercises to further reinforce understanding and prepare students for the exam.
- Experience personalized and adaptive learning with MyMathLab® for School. This innovative program offers interactive practice exercises that provide immediate feedback, ensuring students can learn at their own pace and address any misconceptions.
- With flexible course designs, you can customize the program to fit your specific course requirements, providing a tailored learning experience for your students.
- The comprehensive gradebook and enhanced reporting features allow you to track student progress, identify areas of improvement, and provide targeted support when needed.
- Additionally, the program includes a complete eTextbook that can be accessed anywhere through the Pearson eTextbook app, allowing students to study and review the material at their convenience.
Preface
Guide to AP Calculus
Guide to Mathematical Practices for AP Calculus (MPACs)
AP Calculus Pacing Guide
1. FUNCTIONS
1. Review of Functions
2. Representing Functions
3. Inverse, Exponential, and Logarithmic Functions
4. Trigonometric Functions and Their Inverses
2. LIMITS
1. The Idea of Limits
2. Definitions of Limits
3. Techniques for Computing Limits
4. Infinite Limits
5. Limits at Infinity
6. Continuity
7. Precise Definitions of Limits
3. DERIVATIVES
1. Introducing the Derivative
2. Working with Derivatives
3. Rules of Differentiation
4. The Product and Quotient Rules
5. Derivatives of Trigonometric Functions
6. Derivatives as Rates of Change
7. The Chain Rule
8. Implicit Differentiation
9. Derivatives of Logarithmic and Exponential Functions
10. Derivatives of Inverse Trigonometric Functions
11. Related Rates
4. APPLICATIONS OF THE DERIVATIVE
1. Maxima and Minima
2. What Derivatives Tell Us
3. Graphing Functions
4. Optimization Problems
5. Linear Approximation and Differentials
6. Mean Value Theorem
7. L’Hôpital’s Rule
8. Newton’s Method
5. INTEGRATION
1. Antiderivatives
2. Approximating Areas under Curves
3. Definite Integrals
4. Fundamental Theorem of Calculus
5. Properties of Integrals and Average Value
6. Substitution Rule
7. Numerical Integration
6. APPLICATIONS OF INTEGRATION
1. Velocity and Net Change
2. Regions between Curves
3. Volume by Slicing
4. Volume by Shells
5. Length of Curves
6. Physical Applications
7. INTEGRATION TECHNIQUES
1. Basic Approaches
2. Integration by Parts
3. Partial Fractions
4. Improper Integrals
5. Trigonometric Substitutions
8. DIFFERENTIAL EQUATIONS
1. Basic Ideas
2. Slope Fields and Euler’s Method
3. Separable Differential Equations
4. Exponential Models
9. SEQUENCES AND INFINITE SERIES
1. An Overview
2. Sequences
3. Infinite Series
4. The Divergence and Integral Tests
5. The Ratio, Root, and Comparison Tests
6. Alternating Series
10. POWER SERIES
1. Approximating Functions with Polynomials
2. Properties of Power Series
3. Taylor Series
4. Working with Taylor Series
11. PARAMETRIC, POLAR, AND VECTOR CURVES
1. Parametric Equations
2. Calculus with Parametric Equations
3. Polar Coordinates
4. Calculus in Polar Coordinates
5. Vectors in the Plane
6. Calculus of Vector-Valued Functions
7. Two-Dimensional Motion
Appendix A. Algebra Review
Appendix B. Conic Sections
Appendix C. Proofs of Selected Theorems
Answers
Credits
Index
Table of Integrals
William Briggs
University of Colorado at Denver
For the past 23 years, William Briggs has been a valued member of the mathematics faculty at the University of Colorado at Denver. He holds a BA in mathematics from the University of Colorado, an MS and a PhD in applied mathematics from Harvard University. William's expertise spans across the mathematics curriculum, and he teaches both undergraduate and graduate courses. His focus areas include mathematical modeling and applying differential equations to problems in biosciences.
William has authored several noteworthy publications, including "Using and Understanding Mathematics," a textbook that explores quantitative reasoning. He has also written "Ants, Bikes, and Clocks," a book dedicated to undergraduate problem-solving. Additionally, he has contributed to the field with two tutorial monographs: "The Multigrid Tutorial" and "The DFT: An Owner's Manual for the Discrete Fourier Transform." His dedication to education extends beyond the classroom. William currently serves as the Vice President for Education at the Society for Industrial and Applied Mathematics (SIAM) and is recognized as a University of Colorado President's Teaching Scholar. He has received the prestigious Outstanding Teacher Award from the Rocky Mountain Section of the Mathematical Association of America (MAA). Furthermore, his contributions to the field have been recognized internationally, as he is a recipient of the Fulbright Fellowship to Ireland.
Lyle Cochran
Whitworth University
Lyle Cochran is a distinguished professor of mathematics at Whitworth University in Spokane, Washington. He holds a BS in mathematics and mathematics education from Oregon State University, as well as an MS and PhD in mathematics from Washington State University. Throughout his career, Lyle has taught a wide range of mathematics courses at various institutions, including Washington State University, Fresno Pacific University, and Whitworth University since 1995. His expertise lies in mathematical analysis, with a specific focus on integrating technology into mathematics education.
Lyle has made significant contributions to the field through his authorship of technology materials for renowned calculus and linear algebra textbooks. Notably, he has contributed to the Instructor's Mathematica Manual for "Linear Algebra and Its Applications" by David C. Lay, as well as the Mathematica Technology Resource Manual for "Thomas' Calculus." Lyle is an active member of the Mathematical Association of America (MAA) and has previously served as the chair of the Department of Mathematics and Computer Science at Whitworth University.
Bernard Gillett
University of Colorado at Boulder
Bernard Gillett is a Senior Instructor at the University of Colorado at Boulder, where he has dedicated his career to undergraduate education. With a wealth of experience spanning two decades, Bernard has taught a diverse range of mathematics courses and has been recognized with five prestigious teaching awards. In addition to his teaching accomplishments, Bernard has made significant contributions to educational resources. He authored a software package that focuses on algebra, trigonometry, and precalculus, providing students with valuable tools to enhance their learning experience. He has contributed to the success of "Using and Understanding Mathematics" by Briggs and Bennett by authoring the Student's Guide and Solutions Manual, the Instructor's Guide and Solutions Manual. Bernard has also played a key role in "Calculus and Calculus: Early Transcendentals" by Briggs, Cochran, and Gillett, having authored the Instructor's Resource Guide and Test Bank. Beyond his academic pursuits, Bernard is an enthusiastic rock climber. He has shared his passion for climbing by publishing four climbing guides that cover the mountains in and around Rocky Mountain National Park.
This program is available in a variety of formats. You can review the individual prices for each ISBN in our catalog. All access codes are for use by 1 student, for 1 course, for up to 1 year, and are non-transferable.
| Format | ISBN-13 |
|---|---|
| Student edition | 9780134725765 |
| Student edition + MathXL for School (1-year access) | 9780134717388 |
| Student edition + MathXL for School (6-year access) | 9780134717371 |
| Student edition + MyMathLab for School with Pearson eTextbook (1-year access) | 9780134717364 |
| Student edition + MyMathLab for School with Pearson eTextbook (6-year access) | 9780134717357 |
| Annotated teacher's edition | 9780134705521 |
| MyMathLab for School with Pearson eTextbook (1-year access) | 100% digital solution. Access code is delivered via email. | 9780132962377 |
| MyMathLab for School with Pearson eTextbook (6-year access) | 100% digital solution. Access code is delivered via email. | 9780132962391 |
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