This text takes a rigorous approach to, and therefore creates a deeper understanding of, the usual topics handled in one-dimensional calculus--limits, continuity, differentiation, integration, and infinite series. The text was designed to bridge the gap between intuitive calculus courses normally offered at the undergraduate level and the sophisticated analysis courses offered at the senior or graduate level. The author wrote the book with two goals in mind: the development of a rigorous foundation for the basic topics of analysis, and the less tangible acquisition of an accurate intuitive feeling for analysis.
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This text examines the topics handled in one-dimensional calculus, such as limits, continuity, differentiation, integration, and infinite series. The text was designed to bridge the gap between intuitive calculus courses normally offered at the undergraduate level and the sophisticated analysis courses the student encounters at the senior or graduate level. It has two aims: the development of a fou ndation for the basic topics of analysis, and the acquisition of an accurate intuitive feeling for analysis.
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