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This is a new text covering advanced calculus. It discusses such topics as number systems, the extreme value problem, continuous functions, differentiation, integration and infinite series. The exposition is generally slower pace than that of most other texts, and it provides many examples which are important to students in a first analysis course. The reader will find that the focus of attention is shifted from the learning and applying of computational techniques to careful reasoning from hypothesis to conclusion. The book is intended both for a terminal course and as preparation for more advanced studies in mathematics, science, engineering and computation.