Introduction to Calculus and Analysis I Paperback – Dec 22 1998
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From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. [...]It is the best text known to the reviewer for anyone trying to make an analysis course less abstract." --The Mathematical Gazette
About the Author
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.
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.
Top Customer Reviews
This is not surprising because 1) Courant and John were both important German-born mathematicians, both schooled in that great mathematical mecca, Gottingen, both making fundamental contributions to many classical branches of pure and applied mathematics. Courant is an especially important mathematician since he not only studied under the greats Minkowski and Hilbert - even serving as the latter's assistant - but founded the Courant Institute of Mathematical Sciences in New York, modelled on the Gottingen Mathematical Institute. 2) That typical German thoroughness and emphasis on the mastery of the "fundamental concepts", so dear to German textbooks, is evident in all sections of the book, particularly in the introductory material on the number continuum, functions, continuity etc.
The exercises at the end of chapters are substantial and excellent, and help to develop proof skills in students as well as a subtle mathematical intuition.
Mathematics is best learnt by studying books written by important mathematicians. Classic books like these should always serve to prove the truth of Abel's dictum that to master mathematics one should 'study the masters and not the pupils'.
a /LOT/ of ground with ample explanations and an approach that favours an intuitive understanding of the basic elements of Analysis along with a certain amount of necassary mathematical rigour.
It introduces Integration before Differentiation, which is historically correct and allows one to understand the intricate tie between the two
processes more thoroghly. A pleasure to read.
Most recent customer reviews
Courant and John have done an excellent job in making me a Calculus-and-Analysis fan. The book is very well written, well motivated and easy to understand - even for me, as an... Read morePublished on Sept. 30 2000
This book is maybe a bit old in style, but you can't deny its worth. As a student of electronics I wanted a complement to my ordinary book (swedish). Read morePublished on March 19 2000 by Staffan Bjärle
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