# Calculus: Graphical, Numerical, Algebraic AP Edition 6th Edition © 2020

Calculus: Graphical, Numerical, Algebraic guides students to a deep understanding of advanced mathematical concepts with a structure that prepares them for the AP® examination at the end of the year.

• In-text questions and exercises reflect current AP formats
• Expanded treatment of the derivative as a measure of sensitivity
• New and improved Chapter Opener questions
• More historical nuggets sprinkled throughout

### AP® Calculus Program for High School Students with Digital Resources

Prepare students for the Calculus AB or BC AP exam with a text that reflects the curriculum and pedagogy of an AP course.

### Conceptual Reinforcement

Lessons are structured to encourage deep learning. Some problems suggest students find a solution without a graphing calculator if it isn’t necessarily needed.

### Test Prep

Multiple choice questions now have four options rather than five, and free response questions now better reflect the style and structure students will encounter on the AP® Calculus examination.

### Supportive Flexibility

Course management comes easily with the ability to quickly create and assign homework, quizzes, and tests. Automatic grading goes straight to the online Gradebook so teachers can focus on instruction.

### Emphasis and Reinforcement

Important mathematical concepts are interwoven throughout the chapters to stress how critical they are for calculus and to help students better remember them in the future.

## AP® Calculus Teaching Solutions

• Function Representation
• Chapter Review Exercises
• Derivatives and Linear Equations
• Real-World Behavior
• Understanding Connections
Students work with functions represented graphically, numerically, analytically, or verbally. The course helps them better understand the interconnections among these presentations.
• Deepening Familiarity
Starts with Reasoning with Definitions and Theorems questions that require students to dig more deeply into the concepts of calculus.
• Review Exercises
Review exercises can be assigned for individual practice or to encourage discussion among classmates.
• Treatment of the Derivative
The authors have expanded the treatment of the derivative as a measure of sensitivity. The topic appears in several different sections of the text to emphasize its importance.
• Point-Slope Form
The commitment to point-slope form for linear equations has been enhanced throughout. Their written form highlights the concept of local linearity, critical for understanding differential calculus.
• Modeling Behavior
Students will be able to model real-world behavior and solve a variety of problems using functions, derivatives, and integrals. They also practice effective communication skills by using proper mathematical language and syntax in presenting their solutions.

### Empower Your Math Students with the MyMathLab® Platform from Pearson

MyMathLab® for School from Pearson personalizes learning with online assessments, assignments, an eText, and other resources that can be used in class or at home.

### Learn how Calculus: Graphical, Numerical, Algebraic Helps AP® Math Instruction

Test Preparation

AP® Math Workbook

Available for purchase, the AP Test Prep Workbook follows the College Board’s structure and format so students can go into the examination with confidence.

## Correlation for AP®

Our solutions for AP® are designed to support and correlate the College Board's Course and Exam Descriptions for each corresponding course.

## More About Calculus: Graphical, Numerical, Algebraic

• Franklin D. Demana Author Bio

Frank Demana received his master’s degree in mathematics and his Ph.D. from Michigan State University. He taught for many years at The Ohio State University before retiring as Professor Emeritus of Mathematics. As an active supporter of the use of technology to teach and learn mathematics, he is co-founder of the international Teachers Teaching with Technology (T3) professional development program. He has been the director and co-director of more than \$10 million of National Science Foundation (NSF) and foundational grant activities, including a \$3 million grant from the U.S. Department of Education Mathematics and Science Educational Research program awarded to The Ohio State University. Along with frequent presentations at professional meetings, he has published a variety of articles in the areas of computer- and calculator-enhanced mathematics instruction. Dr. Demana is also co-founder (with Bert Waits) of the annual International Conference on Technology in Collegiate Mathematics (ICTCM). He is co-recipient of the 1997 Glenn Gilbert National Leadership Award presented by the National Council of Supervisors of Mathematics, and co-recipient of the 1998 Christofferson-Fawcett Mathematics Education Award presented by the Ohio Council of Teachers of Mathematics. Dr. Demana co-authored Precalculus: Graphical, Numerical, Algebraic; Essential Algebra: A Calculator Approach; Transition to College Mathematics; College Algebra and Trigonometry: A Graphing Approach; College Algebra: A Graphing Approach; Precalculus: Functions and Graphs; and Intermediate Algebra: A Graphing Approach.

• Bert K. Waits Author Bio
Bert Waits received his Ph.D. from The Ohio State University and taught Ohio State students for many years before retiring as Professor Emeritus of Mathematics. Dr. Waits co-founded the international Teachers Teaching with Technology (T3) professional development program and was co-director or principal investigator on several large projects funded by the National Science Foundation. Active in both the Mathematical Association of America and the National Council of Teachers of Mathematics, he published more than 70 articles in professional journals and conducted countless lectures, workshops, and minicourses on how to use computer technology to enhance the teaching and learning of mathematics. Dr. Waits was co-recipient of the 1997 Glenn Gilbert National Leadership Award presented by the National Council of Supervisors of Mathematics and of the 1998 Christofferson-Fawcett Mathematics Education Award presented by the Ohio Council of Teachers of Mathematics. He was the co-founder (with Frank Demana) of the ICTCM and was one of six authors of the high school portion of the groundbreaking 1989 NCTM Standards. Dr. Waits was hard at work on revisions for the fifth edition of this calculus text when he died prematurely on July 27, 2014, leaving behind a powerful legacy in the legions of teachers whom he inspired. Dr. Waits co-authored Precalculus: Graphical, Numerical, Algebraic; College Algebra and Trigonometry: A Graphing Approach; College Algebra: A Graphing Approach; Precalculus: Functions and Graphs; and Intermediate Algebra: A Graphing Approach.
• Daniel Kennedy Author Bio
Dan Kennedy received his undergraduate degree from the College of the Holy Cross and his master’s degree and Ph.D. in mathematics from the University of North Carolina at Chapel Hill. Since 1973 he has taught mathematics at the Baylor School in Chattanooga, Tennessee, where he holds the Cartter Lupton Distinguished Professorship. Dr. Kennedy joined the Advanced Placement® Calculus Test Development Committee in 1986, then in 1990 became the first high school teacher in 35 years to chair that committee. It was during his tenure as chair that the program moved to require graphing calculators and laid the early groundwork for the 1998 reform of the Advanced Placement Calculus curriculum. The author of the 1997 Teacher’s Guide—AP® Calculus , Dr. Kennedy has conducted more than 50 workshops and institutes for high school calculus teachers. His articles on mathematics teaching have appeared in the Mathematics Teacher and the American Mathematical Monthly , and he is a frequent speaker on education reform at professional and civic meetings. Dr. Kennedy was named a Tandy Technology Scholar in 1992 and a Presidential Award winner in 1995. Dr. Kennedy co-authored Precalculus: Graphical, Numerical, Algebraic; Prentice Hall Algebra I; Prentice Hall Geometry; and Prentice Hall Algebra 2.
• David M. Bressoud Author Bio
David Bressoud received his undergraduate degree from Swarthmore College and Ph.D. from Temple University. He taught at Penn State from 1977 to 1994, is currently DeWitt Wallace Professor of Mathematics at Macalester College, and is a former president of the Mathematical Association of America. He is the author of several texts on number theory, combinatorics, vector calculus, and real analysis, all with a strong historical emphasis. He taught AP© Calculus at the State College Area High School in 1990–91, began as an AP Reader in 1993, and served on the AP Calculus Test Development Committee for six years and as its chair for three of those years. He has been Principal Investigator for numerous grants, including two large National Science Foundation grants to study Characteristics of Successful Programs in College Calculus and Progress Through Calculus. He also writes Launchings, a monthly blog on issues of undergraduate mathematics education, and he is the author of Second Year Calculus: From Celestial Mechanics to Special Relativity (Springer Verlag) and Calculus Reordered: A History of the Big Ideas (Princeton University Press).
• Michael Boardman Author Bio
Michael Boardman is Professor of Mathematics at Pacific University in Oregon where he served seven years as chair of the Department of Mathematics and Computer Science and three years as chair of the Natural Sciences Division. He has been actively involved in AP Calculus since 1994. Boardman was the founding moderator for the AP Calculus Electronic Discussion group and continued in that capacity for a decade. He participated in the AP Calculus Reading each year beginning in 1994, eventually rising to the position of Chief Reader for the years 2008–2011. He served five years on the AP Calculus Development Committee and four additional years on the ETS’s AP Calculus Workgroup. Boardman is co-author, with Roger Nelsen, of College Calculus, a second-term calculus text for college students who successfully completed AP Calculus AB in high school. Boardman currently serves as chair of the Mathematical Association of America’s Committee on the Undergraduate Program in Mathematics (CUPM), the body that publishes recommendations on curriculum for undergraduate mathematics departments. Boardman has been the recipient of grants related to calculus education and also to teacher professional development, and is the recipient of Pacific’s S.S. Johnson Award for Excellence in Teaching.

Chapter 1: Prerequisites for Calculus

• 1.1 Linear Functions
• 1.2 Functions and Graphs
• 1.3 Exponential Functions
• 1.4 Parametric Equations
• 1.5 Inverse Functions and Logarithms
• 1.6 Trigonometric Functions

Chapter 2: Limits and Continuity

• 2.1 Rates of Change and Limits
• 2.2 Limits Involving Infinity
• 2.3 Continuity
• 2.4 Rates of Change, Tangent Lines, and Sensitivity

Chapter 3: Derivatives

• 3.1 Derivative of a Function
• 3.2 Differentiability
• 3.3 Rules for Differentiation
• 3.4 Velocity and Other Rates of Change
• 3.5 Derivatives of Trigonometric Functions

Chapter 4: More Derivatives

• 4.1 Chain Rule
• 4.2 Implicit Differentiation
• 4.3 Derivatives of Inverse Trigonometric Functions
• 4.4 Derivatives of Exponential and Logarithmic Functions

Chapter 5: Applications of Derivatives

• 5.1 Extreme Values of Functions
• 5.2 Mean Value Theorem
• 5.3 Connecting ƒ_ and ƒ _ with the Graph of ƒ
• 5.4 Modeling and Optimization
• 5.5 Linearization, Sensitivity, and Differentials
• 5.6 Related Rates

Chapter 6: The Definite Integral

• 6.1 Estimating with Finite Sums
• 6.2 Definite Integrals
• 6.3 Definite Integrals and Antiderivatives
• 6.4 Fundamental Theorem of Calculus
• 6.5 Trapezoidal Rule

Chapter 7: Differential Equations and Mathematical Modeling

• 7.1 Slope Fields and Euler’s Method
• 7.2 Antidifferentiation by Substitution
• 7.3 Antidifferentiation by Parts
• 7.4 Exponential Growth and Decay
• 7.5 Logistic Growth

Chapter 8: Applications of Definite Integrals

• 8.1 Accumulation and Net Change
• 8.2 Areas in the Plane
• 8.3 Volumes
• 8.4 Lengths of Curves
• 8.5 Applications from Science and Statistics

Chapter 9: Sequences, L’Hospital’s Rule, and Improper Integrals

• 9.1 Sequences
• 9.2 L ’Hospital’s Rule
• 9.3 Relative Rates of Growth
• 9.4 Improper Integrals

Chapter 10: Infinite Series

• 10.1 Power Series
• 10.2 Taylor Series
• 10.3 Taylor’s Theorem
• 10.4 Radius of Convergence
• 10.5 Testing Convergence at Endpoints

Chapter 11: Parametric, Vector, and Polar Functions

• 11.1 Parametric Functions
• 11.2 Vectors in the Plane
• 11.3 Polar Functions

Appendices

• A1 Formulas from Precalculus Mathematics
• A2 A Formal Definition of Limit
• A3 A Proof of the Chain Rule
• A4 Hyperbolic Functions
• A5 A Very Brief Table of Integrals

Glossary

Applications Index

Subject Index

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