Introduction to Calculus and Analysis, Vol. II/1 (Classics in Mathematics) 2000th Edition by Richard Courant (PDF)

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From the reviews: “…one of the best textbooks introducing several generations of mathematicians to higher mathematics. … This excellent book is highly recommended both to instructors and students.” –Acta Scientiarum Mathematicarum, 1991

User’s Reviews

Editorial Reviews: Review From the reviews: “These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures…Of interest to students, mathematicians, scientists and engineers. Even more than that.” Newsletter on Computational and Applied Mathematics, 1991 “…one of the best textbooks introducing several generations of mathematicians to higher mathematics. … This excellent book is highly recommended both to instructors and students.” Acta Scientiarum Mathematicarum, 1991 From the Back Cover Biography of Richard CourantRichard 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 JohnFritz 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)

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐It’s a marvellous classic on the subject renewed in this prestigious edition by Springer. I hope I can get the other volumes soon: 1 and II/2.

⭐I bought this, at age 17, as my first calculus book. I found it very hard and took months to make my way through the first two chapters. I think I retained very little from that first reading, though some things, such as the importance of mean-value theorems, stuck with me even then.It is only now, having had studied analysis from standard books such as Rudin, that I have really come to appreciate this book. The strength of this book lies in the deft way in which concrete mathematical problems and applications from physics are mixed with the general theory. This book makes calculus and analysis come alive as a part of the mathematical sciences.Technique here is kept to a minimum necessary without sacrificing rigour. For example, in Rudin’s ‘Principles’ Stirling’s formula is given as an application of the Gamma function. I found it very hard to understand from that book why the approximation works. Courant and John on the other hand give an elementary derivation using the trapezoid formula for approximating an integral. There are pictures even.While perhaps only the very mathematically gifted can use this as an introduction to calculus and analysis it is an invaluable complement to a more traditional undergraduate analysis textbook.

⭐I give 5 stars to this book because it gives the reader the perfect combination between rigor and intuition. Volume 2 has solutions to almost all the exercises, which is great because some of the problems are very difficult. I really think this is a “must have” text for anyone who wants to learn calculus at a deep level.

⭐On August 1, 2011, Congress amended the CPSIA to exclude ordinary books and ordinary paper-based printed materials from the third party testing and certification requirements of the CPSIA. An “ordinary book” as defined by the amendment, means: “a book printed on paper or cardboard, printed with inks or toners, and bound and finished using a conventional method, and that is intended to be read or has educational value.” H.R.2715.The manufacturer of the book containing this web address only manufactures ordinary books bound and finished in a conventional manner; thus, the books produced by this manufacturer are not subject to the testing and certification requirements of the CPSIA.

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