Integrated Calculus

This unique Calculus textbook presents a comprehensive treatment of single-variable calculus with an emphasis on applications and real-world motivation of the abstract mathematical concepts. As part of the applications, substantial content from elementary ordinary differential equations is also developed. This textbook covers all of the topics expected in a traditional calculus course, and does so in a manner that distinguishes it from much of the existing literature. Specifically, integration and differentiation are introduced immediately and developed in parallel as a unified whole; series and sequences are introduced very early and used throughout; Leibniz notation is introduced later and with great care; pattern recognition is emphasized as a tool for finding antiderivatives, with formal substitutions deemphasized. A wide variety of exercises will aid students with varying levels of ability, motivation, and interest, to solidify understanding of the material. This book will be ideal for a range of instructing styles, as the presentation of topics is flexible, and it may be used both in the university and high school settings.