This is one of the most important and influential books on calculus ever written. It has been reprinted more than twenty times and translated into several other languages, including Russian, and published in the Soviet Union and many other places. We especially want to thank Marvin Jay Greenberg, Emeritus Professor of Mathematics, University of California at Santa Cruz, for his Appendix on Infinitesimals, which includes recent discoveries on Hyperreals and Nilpotent Infinitesimals, and for his bibliography and references, which include up-to-date references to current publications in 2010. This foreword, which includes new mathematical discoveries, is included in Volume One of this work. A professor of mathematics writes: "I've enjoyed with great pleasure your foreword, discovering many interesting things about Courant's life and his thoughts. In particular, your citations about the antithesis between intuition and rigor were very illuminating, because it corresponds to the methodological thread I'm trying to follow developing the theory of Fermat reals. "Infinitesimals without "mysticism", explicit or fogged into unclear logical methods, seems possible. Now, I think we can make a step further, because the rigor increases our possibility to understand."
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Richard Courant was born 8 Jan 1888 in what was then Germany and died on Jan 27, 1972 in New York. His translator, Edward James McShane, was born 10 May 1904 and died in Charlottesville, Virginia on June 1, 1989. Richard Courant (1888 - 1972) was born in Lublinitz, now part of Poland but then in Germany. He studied in Göttingen, which was for many years the capital of the mathematical world, its most prominent scholar being David Hilbert. Courant became Hilbert's assistant there and wrote a doctoral thesis in 1910 under Hilbert's direction, entitled (in English) "On the application of Dirichlet's principle to the problems of conformal mappings." Fourteen years later they published a joint work, subsequently translated into English as Methods of Mathematical Physics (two volumes, volume 2 published much later). It was based on lectures of Hilbert but even more on Courant's own research. It fortuitously contained much of the mathematics needed to understand and solve Schrödinger's equations, discovered two years later. This was a striking example of mathematics anticipating the needs of a new physical theory.
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