This volume contains more than 900 problems in differential calculus, covering limits, continuity, derivatives, and their applications. The applications are comprised of a variety of approximations, growth and decay, optimization, curve sketching techniques, and analytical tools to investigate properties of parametrically given planar curves. The problems are sorted by topic, each opening with with a summary of the relevant mathematical notions and their properties. Through a careful selection of appropriate problems in each chapter, the book clearly communicates some of the big ideas and applications in calculus: the notion of a function, the notion of an infinitesimal, the notion of a differentiable function, and the notion of an approximation, among others. The book provides the answers to each problem, often with a detailed sketch of the solution process.

With about 260 true-false and multiple-choice questions, the book provides its users with an accessible way to assess and practice their understanding of calculus related facts and nuances. More than 180 figures are included to help readers to visualize properties of functions, illustrate word problems, depict solutions, and provide an extensive bank of polar curves.

The purpose of this problem collection is to serve as a supplementary learning resource for students who are studying university-level differential calculus. The book also acts as a teaching resource for calculus instructors.

Contents:

• Preface


• About the Authors


• Preliminaries


• Limits and Continuity


• Derivatives


• Functions and Their Graphs


• Optimization


• Other Applications of Differentiation


• Parametric and Polar Curves


• True–False and Multiple Choice Questions


• Recommendations to Thrive in Mathematics


• Bibliography


• Index

Readership: High school and undergraduate students taking a first-level calculus course as well as high school teachers and calculus instructors. Anyone, e.g., employees in industry who need a refresher in differential calculus, or as a quick reference, or need to further their understanding in certain areas of calculus.

Key Features:

• This book is a cross between a reference book, a learning guide, and a rich learning and teaching resource


• This is a reader-friendly book geared towards undergraduate students, who want to practice calculus problems to understand the subject more deeply but also to prepare themselves for examinations


• The differential calculus problems range from routine to not-so-routine questions, thereby not only providing practice but a deeper dive into the subject


• Each chapter starts with a summary of the relevant mathematical notions and their properties


• Most notably, problems and their solutions are purposefully created to address some of the nuances that may evade a student's (or instructor's) attention in a general calculus course


• The content of the questions is broadly designed for students enrolled in either a science program (mathematics, physics, statistics, chemistry, earth sciences, kinesiology, life sciences) or applied science program (engineering, computing science)


• This book is written for students who are at the beginning of their academic careers. Therefore, the last chapter contains a detailed list of recommendations to guide students in their well-being and approach to learning to become successful academically


• This book is a mathematical text containing precise and consistent mathematical notation and vocabulary throughout. Checking the given properties before applying certain techniques as a crucial step in mathematical thinking is one of the main general messages that this book contains