Introduction to Calculus and Analysis

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Springer Science & Business Media, 2000 - Mathematics - 556 pages
5 Reviews

Biography of Richard Courant

Richard Courant was born in 1888 in a small town of what is now Poland, and died in New Rochelle, N.Y. in 1972. He received his doctorate from the legendary David Hilbert in Göttingen, where later he founded and directed its famed mathematics Institute, a Mecca for mathematicians in the twenties. In 1933 the Nazi government dismissed Courant for being Jewish, and he emigrated to the United States. He found, in New York, what he called "a reservoir of talent" to be tapped. He built, at New York University, a new mathematical Sciences Institute that shares the philosophy of its illustrious predecessor and rivals it in worldwide influence.
For Courant mathematics was an adventure, with applications forming a vital part. This spirit is reflected in his books, in particular in his influential calculus text, revised in collaboration with his brilliant younger colleague, Fritz John.
(P.D. Lax)

Biography of Fritz John

Fritz John was born on June 14, 1910, in Berlin. After his school years in Danzig (now Gdansk, Poland), he studied in Göttingen and received his doctorate in 1933, just when the Nazi regime came to power. As he was half-Jewish and his bride Aryan, he had to flee Germany in 1934. After a year in Cambridge, UK, he accepted a position at the University of Kentucky, and in 1946 joined Courant, Friedrichs and Stoker in building up New York University the institute that later became the Courant Institute of Mathematical Sciences. He remained there until his death in New Rochelle on February 10, 1994.
John's research and the books he wrote had a strong impact on the development of many fields of mathematics, foremost in partial differential equations. He also worked on Radon transforms, illposed problems, convex geometry, numerical analysis, elasticity theory. In connection with his work in latter field, he and Nirenberg introduced the space of the BMO-functions (bounded mean oscillations). Fritz John's work exemplifies the unity of mathematics as well as its elegance and its beauty.
(J. Moser)

  

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Contents

I
1
II
3
III
6
IV
9
VI
11
VII
12
VIII
13
IX
17
LXXXIX
273
XC
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XCI
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XCII
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XCIII
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XCIV
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XCV
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XCVI
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X
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XIII
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XIV
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XXX
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XXXIV
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XLI
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L
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LI
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LIII
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LIV
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LV
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LVI
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LVIII
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LIX
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LXI
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LXXIX
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LXXX
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LXXXI
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LXXXII
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LXXXIII
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LXXXIV
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LXXXV
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LXXXVI
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LXXXVII
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LXXXVIII
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XCVII
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XCVIII
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XCIX
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C
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CI
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CII
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CIII
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CIV
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CV
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CVI
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CVII
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CVIII
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CIX
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CX
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CXI
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CXV
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CXXIII
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CXXV
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CXXVII
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CXXVIII
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CXXIX
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CXXX
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CXXXI
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CXXXII
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CXXXIV
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CXXXV
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CXXXVI
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CXXXIX
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CXL
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CXLI
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CXLIII
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CXLIV
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CXLV
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CXLVI
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CXLIX
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CL
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CLI
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CLII
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CLIII
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CLIV
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CLV
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CLVI
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CLVII
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CLIX
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CLX
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CLXI
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CLXIII
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CLXIV
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CLXV
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CLXIX
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CLXX
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CLXXI
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CLXXII
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CLXXIII
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CLXXIV
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CLXXV
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About the author (2000)

Richard Courant was born in Lublintz, Germany, on January 8, 1888, later becoming an American citizen. He was a mathematician, researcher and teacher, specializing in variational calculus and its applications to physics, computer science, and related fields. He received his Ph.D. from the University of Gottingen, Germany, lectured at Cambridge University and headed the mathematics department at New York University. Courant's writings include Introduction to Calculus and Analysis (1965), written with John Fritz, Differential and Integral Calculus (1965), Methods of Mathematical Physics: Dirichlet's Principle, Conformal Mapping and Minimal Surfaces (1950), and Supersonic Flow and Shock Waves (1948). He edited a mathematics series and contributed to journals and periodicals. Courant received the Distinguished Service Award from the Mathematical Association of America in 1965. He earned the Navy Distinguished Public Service Award, the Knight-Commander's cross, and Germany's Star of the Order of Merit in 1958. Courant died on January 27, 1972.

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