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.