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One of the twentieth century's most original mathematicians and thinkers, Karl Menger taught students of many backgrounds. In this, his radical revision of the traditional calculus text, he presents pure and applied calculus in a unified conceptual frame, offering a thorough understanding of theory as well as of the methodology underlying the use of calculus as a tool.The most outstanding feature of this text is the care with which it explains basic ideas, a feature that makes it equally suitable for beginners and experienced readers. The text begins with a "mini-calculus" which brings out the fundamental results without recourse to the notions of limit and continuity. The standard subject matter is then presented as a pure and unambiguous calculus of functions. The issues surrounding the applications of pure calculus to problems in the sciences are faced in a forthright manner by carefully analyzing the meaning of "variable quantity" and clarified by resuscitating Newton's concept of fluents. The accompanying exercises are original, insightful and an integral part of the text. This Dover edition features a new Preface and Guide to Further Reading by Bert Schweizer and Abe Sklar.