Mathematical Methods in Science

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Cambridge University Press, 1977 - Science - 234 pages
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'Mathematics, taught and learned appropriately, improves the mind and implants good habits of thought.' This tenet underlies all of Professor Pólya's works on teaching and problem-solving. This book captures some of Pólya's excitement and vision. In it he provides enlightenment for all those who have ever wondered how the laws of nature were worked out mathematically. The distinctive feature of the present book is the stress on the history of certain elementary chapters of science; these can be a source of enjoyment and deeper understanding of mathematics even for beginners who have little, or perhaps no, knowledge of physics.
  

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Contents

INTRODUCTION
1
SUCCESSIVE APPROXIMATION
32
From the History of Statics
47
section J VECTORS
58
From the History of Dynamics
82
NEWTON
105
THE PENDULUM
125
Physical Reasoning in Mathematics
159
POWER SERIES
192
PHYSICAL ANALOGY
224
Copyright

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About the author (1977)

Biography of George Polya
Born in Budapest, December 13, 1887, George Polya initially studied law, then languages and literature in Budapest. He came to mathematics in order to understand philosophy, but the subject of his doctorate in 1912 was in probability theory and he promptly abandoned philosophy.
After a year in Gottingen and a short stay in Paris, he received an appointment at the ETH in Zurich. His research was multi-faceted, ranging from series, probability, number theory and combinatorics to astronomy and voting systems. Some of his deepest work was on entire functions. He also worked in conformal mappings, potential theory, boundary value problems, and isoperimetric problems in mathematical physics, as well as heuristics late in his career. When Polya left Europe in 1940, he first went to Brown University, then two years later to Stanford, where he remained until his death on September 7, 1985.


Biography of Gabor Szego
Born in Kunhegyes, Hungary, January 20, 1895, Szego studied in Budapest and Vienna, where he received his Ph. D. in 1918, after serving in the Austro-Hungarian army in the First World War. He became a privatdozent at the University of Berlin and in 1926 succeeded Knopp at the University of Ksnigsberg. It was during his time in Berlin that he and Polya collaborated on their great joint work, the Problems and Theorems in Analysis. Szego's own research concentrated on orthogonal polynomials and Toeplitz matrices. With the deteriorating situation in Germany at that time, he moved in 1934 to Washington University, St. Louis, where he remained until 1938, when he moved to Stanford. As department head at Stanford, he arranged for Polya to jointhe Stanford faculty in 1942. Szego remained at Stanford until his death on August 7, 1985.

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