Differential Calculus

This volume contains more than 900 problems that cover topics in differential calculus: 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 with a summary of the relevant mathematical notions and their properties at the beginning. 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. All problems are accompanied with their answers and, most frequently, with either a sketch of the solution process or detailed solutions.With about 260 true-false and multiple-choice questions, the book provides to its users an accessible way to check out their understanding of calculus related facts as well as nuances and practice them. To help the reader, more than 180 figures are woven throughout the book 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 taking a university-level differential calculus course. In addition, the book provides a teaching resource for calculus instructors.