Worldwide Single-Variable Calculus
for AP® Calculus

David B. Massey




Worldwide Single-Variable Calculus
for AP® Calculus

Worldwide AP Calculus
David B. Massey– Northeastern University

ISBN-10: 0-9842071-6-3
ISBN-13: 978-0-9842071-6-9
680 Pages
©2011 Worldwide Center of Mathematics, LLC

Digital PDF | $14.95
Print BW | $39.95


"Worldwide AP Calculus" takes, what has become, a non-standard approach in the topics covered and their ordering. The textbook does not try to “teach to the test.” An Advanced Placement course is designed to provide students with the necessary background and skills for advanced placement into their respective college curricula. Too often, modern AP Calculus textbooks have one goal: to optimize students' grades on the AP Calculus exam, regardless of how well the students may end up being prepared to be placed at advanced points in college curricula.

Thus, the content in "Worldwide AP Calculus" is the same material that students would see when using a Calculus textbook in a college or university; so that, while they will be prepared for the AP exam at the end of the course, they will also have the knowledge they need to move on to higher-level math courses when they enter college. The book is a combination of Massey’s Worldwide Differential Calculus and Worldwide Integral Calculus for easier use in the AP Calculus classroom setting. This textbook can be used in both an AB and a BC course, and also allows students who are continuing on to AP Calculus BC, after completing AB, to need only one textbook for both courses.

The chatty exposition throughout "Worldwide AP Calculus" is meant to make the textbook more readable for students. However, despite the informal style in the discussions, the mathematics in "Worldwide AP Calculus" is completely rigorous. The precise, rigorous statements of definitions, theorems, and proofs are intended to eliminate the confusion caused by the ambiguity and imprecision of many current AP Calculus textbooks. While we do not expect students to be held accountable on tests for so many technicalities, we feel that it is an important aspect of any mathematics course for the students to understand that the mathematically rigorous statements and results actually exist; furthermore, "Worldwide AP Calculus" provides a resource for those students and teachers who are interested in a deeper, more careful, study of Calculus, beyond what will be tested.

Digital resources also set this book apart from the alternatives. At the beginning of each section, there is a full-length lecture video by the author, which provides additional help to students, while also allowing students to keep up with the course if they miss a class. In addition, there are 5-10 selected exercise video-solutions at the end of each section, for students to watch if they have trouble on homework problems. All of these resources are linked to in the .pdf version of the book, but are also available on our YouTube channel for fast and reliable viewing.


Intro Video





Chapter 1 Rates of Change and the Derivative
1.1 Average Rates of Change
1.1.1 Exercises
1.2 Prelude to IROC's
1.2.1 Exercises
1.3 Limits and Continuity
1.3.1 Limits
1.3.2 Continuous Functions
1.3.3 Limits involving Infinity
1.3.4 Exercises
1.4 IROC's and the Derivative
1.4.1 Exercises
1.5 Extrema and the Mean Value Theorem
1.5.1 Exercises
1.6 Higher-Order Derivatives
1.6.1 Exercises

Chapter 2 Basic Rules for Calculating Derivatives
2.1 The Power Rule and Linearity
2.1.1 Exercises
2.2 The Product and Quotient Rules
2.2.1 Exercises
2.3 The Chain Rule and Inverse Functions
2.3.1 Exercises
2.4 The Exponential Function
2.4.1 Exercises
2.5 The Natural Logarithm
2.5.1 Exercises
2.6 General Exponential and Logarithmic Functions
2.6.1 Exercises
2.7 Trigonometric Functions: Sine and Cosine
2.7.1 Exercises
2.8 The Other Trigonometric Functions
2.8.1 Exercises
2.9 Inverse Trig Functions
2.9.1 Exercises
2.10 Implicit Functions
2.10.1 Exercises

Chapter 3 Applications of Differentiation
3.1 Related Rates
3.1.1 Exercises
3.2 Graphing
3.2.1 Exercises
3.3 Optimization
3.3.1 Exercises
3.4 Linear Approximation
3.4.1 Exercises
3.5 l'Hôpital's Rule
3.5.1 Exercises

Chapter 4 Anti-differentiation & Differential Equations
4.1 Basic Anti-Differentiation
4.1.1 Exercises
4.2 Integration by Partial Fractions
4.2.1 Exercises
4.3 What is a Differential Equation?
4.3.1 Exercises
4.4 Separable Differential Equations
4.4.1 Exercises
4.5 Approximating Solutions
4.5.1 Exercises

Chapter 5 Continuous Sums: the Definite Integral
5.1 Sums and Differences
5.1.1 Exercises
5.2 Prelude to the Definite Integral
5.2.1 Exercises
5.3 The Definite Integral
5.3.1 Exercises
5.4 The Fundamental Theorem of Calculus
5.4.1 Exercises
5.5 Improper Integrals
5.5.1 Exercises
5.6 Numerical Techniques
5.6.1 Exercises

Chapter 6 Applications of Integration
6.1 Displacement and Distance Traveled
6.1.1 Exercises
6.2 Area in the Plane
6.2.1 Exercises
6.3 Distance Traveled in Space and Arc Length
6.3.1 Exercises
6.4 Area Swept Out and Polar Coordinates
6.4.1 Exercises
6.5 Volume
6.5.1 Exercises
6.6 Surface Area
6.6.1 Exercises
6.7 Mass and Density
6.7.1 Exercises

Chapter 7 Polynomials and Power Series
7.1 Approximating Polynomials
7.1.1 Exercises
7.2 Approximation of Functions
7.2.1 Exercises
7.3 Error in Approximation
7.3.1 Exercises
7.4 Functions as Power Series
7.4.1 Exercises
7.5 Power Series as Functions I
7.5.1 Exercises
7.6 Power Series as Functions II
7.6.1 Exercises

Chapter 8 Theorems on Sequences and Series
8.1 Theorems on Sequences
8.1.1 Exercises
8.2 Basic Theorems on Series
8.2.1 Exercises
8.3 Non-negative Series
8.3.1 Exercises
8.4 Series with Positive and Negative Terms
8.4.1 Exercises

Appendix A Parameterized Curves and Motion
A.1 Parameterized Curves
A.1.1 Exercises
Appendix B Tables of Derivative Formulas
Appendix C Tables of Integration Formulas
Appendix D Answers to Odd-Numbered Problems




- Written by an award-winning mathematics professor with 30 years of teaching experience

- Down-to-Earth exposition, presented as it would be spoken in class

- Completely rigorous definitions, statements of theorems, and proofs

- Technical proofs at the end of each chapter, to avoid disrupting the exposition

- Margin side-remarks and historical references

- Hyperlinked table of contents, index, and cross-references

- Embedded video links to full-length lectures

- Video-solutions to select exercises

- PDF format, compatible with all computers, tablets, and mobile devices

- Low cost in electronic or print form





  • Faculty Solution Manual (Free)
    Faculty can request a free faculty solution manual by contacting

    Worldwide AP Calculus Study Guide (free with textbook | $7.95) go >
    The study guide for Worldwide AP Calculus contains a full-length video lecture for each section of the textbook, ideas and definitions, formulas and theorems, remarks and warnings, and video exercise solutions for each topic.

    Full-length lecture videos (Free) go >
    Full lecture videos on the core material from each section are available on the video portion of our website and YouTube.  There are also direct links within the textbook to each corresponding video.

    AP Calculus Study Guide iOS app ($0.99) go >
    The AP Calculus Reference Guide includes a number of features all of which are designed to help students prepare for the AB and BC Advanced Placement Calculus College Board exams.  Features include full-length video lectures, exercise examples and solution videos for practice or review, and a full glossary for every theorem or definition covered on the exam.




2012-2013 School Year
Student Testimonials

"The video solutions were extremely helpful."

"To bring around your textbook on your laptop is quite helpful, and it's one less heavy book to carry."

"[The video resources] were easy to understand. I prefer to watch lectures than just read the text."

"The topics were very useful when it came to preparing for the AP exam."

"I enjoyed the video resources as it helps to see someone walking through the problems."

"I liked seeing the problems done step-by-step so that I would work through them along with the videos."




David Massey
David B. Massey received his Ph.D. in mathematics in 1986 for his results in the area of complex analytic singularities. He taught for two years at Duke as a graduate student, and then for two years, 1986-1988, as a Visiting Assistant Professor at the University of Notre Dame. In 1988, he was awarded a National Science Foundation Postdoctoral Research Fellowship, and went to conduct research on singularities at Northeastern University. In 1991, he assumed a regular faculty position in the Mathematics Department at Northeastern. He has remained at Northeastern University ever since, where he is now a Full Professor.