Through a rigorous approach to the usual topics handled in one-dimensional calculus--limits, continuity, differentiation, integration, and infinite series--this text offers a deeper understanding of those concepts. The text is designed so that students come away from the course with a rigorous foundation for the basic topics of analysis. The exercise sets in this edition were expanded to give students additional opportunities for practice. Students are encouraged to pay particular attention to the exercises that have been marked with stars, because they are vital to the development of later sections. "Projects", appearing at the end of each chapter, present more challenging, multi-step problems.