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Advanced Calculus by Gerald B. Folland - Rocking Book Reads
Advanced Calculus by Gerald B. Folland. Excellent Book. This book presents a
unified view of calculus in which theory and practice reinforces each other.
Advanced Calculus by Gerald B. Folland
Excellent Book
This book presents a unified view of calculus in which theory and practice reinforces each other. It is about the theory and applications of derivatives (mostly partial), integrals, (mostly multiple or improper), and infinite series (mostly of functions rather than of numbers), at a deeper level than is found in the standard calculus books. Chapter topics cover: Setting the Stage, Differential Calculus, The Implicit Function Theorem and Its Applications, Integral Calculus, Line and Surface Integrals —Vector Analysis, Infinite Series, Functions Defined by Series and Integrals, and Fourier Series. For individuals with a sound knowledge of the mechanics of one-variable calculus and an acquaintance with linear algebra. I was a T.A for a course for which this was the textbook. I found this book a joy to read. The proofs are very careful and rigorous, but they also omit details which would otherwise halt the flow of the text. The omissions are made only where the author has already prepared the reader to fill in the gaps. The nice flow allows the reader to catch the ideas behind the proofs. The author motivates the theorems and proofs very well, making clever ideas transparent and natural. This prepares the reader for future studies. The book includes very interesting sections on more advanced topics like the Gamma function, Stirling's formula and Fourier series. If you just want a good grade in your course, this may not be the best book for you, but if you really want to learn something, this book is perfect.
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