A First Course in Real Analysis (Undergraduate Texts in by Sterling K. Berberian

By Sterling K. Berberian

arithmetic is the tune of technological know-how, and actual research is the Bach of arithmetic. there are various different silly issues i'll say concerning the topic of this publication, however the foregoing will supply the reader an idea of the place my center lies. the current booklet was once written to help a primary direction in actual research, ordinarily taken after a yr of effortless calculus. actual research is, approximately talking, the fashionable surroundings for Calculus, "real" alluding to the sphere of actual numbers that underlies all of it. At heart level are services, outlined and taking values in units of genuine numbers or in units (the airplane, 3-space, etc.) with no trouble derived from the true numbers; a primary path in actual research commonly locations the emphasis on real-valued features outlined on units of genuine numbers. The schedule for the path: (1) begin with the axioms for the sphere ofreal numbers, (2) construct, in a single semester and with acceptable rigor, the foun­ dations of calculus (including the "Fundamental Theorem"), and, alongside the best way, (3) strengthen these abilities and attitudes that permit us to continue to learn arithmetic on our personal. 3 many years of expertise with the workout haven't decreased my astonishment that it may be done.

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