Worldwide Differential Calculus

David B. Massey




Worldwide Differential Calculus

Worldwide Differential Calculus
David B. Massey – Northeastern University

ISBN-10: 0-9842071-9-8
ISBN-13:  978-0-9842071-9-0
565 Pages
© Worldwide Center of Mathematics, LLC

Digital PDF | $14.95
Print BW | $39.95


Differential Calculus is the study of instantaneous rates of change; these rates of change are known as derivatives. This book is written by David B. Massey, Ph.D., an award-winning teacher and world-renowned research mathematician, who has been teaching college students for 30 years. He emphasizes intuitive ideas in conjunction with rigorous statements of theorems, and provides a large number of illustrative examples. In the accompanying videos, Dr. Massey lectures on the core material from each section.




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
Appendix 1.A Technical Matters
1.A.1 Properties of Real Numbers and Extended Real Numbers
1.A.2 Functions
1.A.3 Proofs of Theorems on Limits and Continuity
1.A.4 Proofs of Theorems on Differentiability and Continuity

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
Appendix 2.A Technical Matters

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
Appendix 3.A Technical Matters

Chapter 4 Anti-differentiation & Differential Equations
4.1 What is a Differential Equation?
4.1.1 Exercises
4.2 Anti-derivatives
4.2.1 Exercises
4.3 Separable Differential Equations
4.3.1 Exercises
4.4 Applications of Differential Equations
4.4.1 Exercises
4.5 Approximating Solutions
4.5.1 Exercises

Appendix A Parameterized Curves and Motion
A.1 Parameterized Curves
A.1.1 Exercises
Appendix B Tables of Derivative Formulas
Appendix C 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 Differential Calculus Study Guide (free with textbook | $4.95) go >
The study guide for Worldwide Differential Calculus contains a full-length video lecture for each section of the textbook, ideas and definitions, formulas and theorems, remarks and warnings, and example problems for each topic. It also contains margin side-remarks and historical references.

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.

WebAssign Online Homework and Grading go >
WebAssign is the leading provider of powerful online instructional tools for faculty and students. Students enter their answers online, and WebAssign automatically grades the assignment and gives students instant feedback on their performance. Much more than just a homework grading system, WebAssign delivers secure online testing, customizable pre-coded questions from a wide range of math and science textbooks, and unparalleled customer service.

Differential Calculus Study Guide iOS app ($0.99) go >
The Differential Calculus Reference Guide includes a number of features all of which are designed to help students learn outside of the classroom. Features include full-length video lectures, full glossary for every theorem or definition covered in Calc I, and hyperlinked navigation.




Student Testimonials:
Taken from anonymous surveys dis­tributed by faculty members at the end of the course after implementing the Worldwide Calculus eTextbooks.

“Watching the lectures before class was really helpful and allowed me to grasp the concepts better in class.”

“The videos were extremely convenient. They were basically full lectures that could be watched at any time. When I was com­fortable with a concept, I could easily skip through it in the video and move on to harder concepts.”

“I watched the videos when I missed class or didn’t understand the topic well enough. The videos supplemented the material suf­ficiently and well.”

“I liked the writing, especially how the fi­nal theorems were boxed so they were easy to find.”

“The calculus book covers a broad range of topics. The writing in the book is very easy to read and conversational.”

“The explanations of each topic were thorough, especially the proofs. It was good to see it explained in theory and ap­plication.”

Faculty Testimonials:
“I love your concept - it has the potential to become a very, very unique look at Calculus within the context of our entire world.”
High School Teacher

“I like the flow of the book. The progression makes sense and it keeps teachers from jumping around from chapter to chapter.”
High School Teacher

“It provides such a cost effective way to provide a textbook to my calculus students.”
University Professor

“I like the friendly and lecture style presentation of the book.”
University Professor

“The author has put more thought than other authors into examples and solutions. He does a good job to using examples to motivate mathematical concepts.”




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.