The Calculus: A Genetic Approach

Published by the U. of Chicago Press in association with the Mathematical Association of America, this is a reprint of Toeplitz' 1963 classic work (that is, the translation from the German edition into English, published by Springer Verlag); it includes a new foreword by David Bressoud. The original is listed as "highly recommended" in Library Recommendations for Undergraduate Mathematics. Following the main currents of calculus, the approach is historical, but this is not a history (no blind alleys). It is appropriate for students who have completed basic or high school calculus but have not yet stepped up to the rigors of advanced calculus. Here those students will find motivation for understanding techniques in response to the original problems that gave rise to them. For example, the study of limits can seem arbitrary, but Toeplitz' discussion offers background on why the Greeks thought they were interesting and what problems they address. ("Genetic" in the subtitle refers to genesis, rather than anything to do with biology.) Annotation c2008 Book News, Inc., Portland, OR (booknews.com)