Designed to be readable and intimidation-free, this advanced calculus book presents material that flows logically allowing readers to grasp concepts and proofs. Providing in-depth discussion of topics, the book also features common errors to encourage caution and easy recall of errors. It also presents many proofs in great detail and those which should not provide difficulty are either short or simply outlined. Throughout the book, there are a number of important and useful features, such as cross-referenced functions, expressions, and ideas; footnotes which place mathematical development in historical perspective; an index of symbols; and definitions and theorems which are clearly stated and well marked. An important reference for every professional who uses advanced math.
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Designed to be readable and intimidation-free, this advanced calculus book presents material that flows logically allowing readers to grasp concepts and proofs. Providing in-depth discussion of topics, the book also features common errors to encourage caution and easy recall of errors. It also presents many proofs in great detail and those which should not provide difficulty are either short or simply outlined. Throughout the book, there are a number of important and useful features, such as cross-referenced functions, expressions, and ideas; footnotes which place mathematical development in historical perspective; an index of symbols; and definitions and theorems which are clearly stated and well marked. An important reference for every professional who uses advanced math.
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Most Helpful Customer Reviews
21 of 21 people found the following review helpful:
5.0 out of 5 stars
A perfect place to start...,
By Charles Wavada (St. Louis, MO USA) - See all my reviews
This review is from: Advanced Calculus: A Friendly Approach (Hardcover)
This may be the best available introduction to Advanced Calculus and Real Analysis. It is well-organized, well-written, and provides a lot of explanatory text for each topic, theorem, and proof. I have copies of Rudin, Apostol, Bear, Fulks, and Protter, but this book beats them all as an introductory text. If you are looking for a self-study text, or if you want a reference companion to help you understand Rudin or Apostol, try this book first. You won't be disappointed.
24 of 25 people found the following review helpful:
5.0 out of 5 stars
Worth buying,
By AbuHasan Chan (Malaysia) - See all my reviews
This review is from: Advanced Calculus: A Friendly Approach (Hardcover)
Advanced Calculus is the version of Calculus treated with mathematical rigor. Today's Elementary Calculus books are written in such a way as to make Calculus itself will seem less frightening and is user friendly, especially with the use new technology. When stepping into the realm of Advanced Calculus, one must be prepared to endure having to read and give proofs to many theorems. Then the so-called Advanced Calculus is a very dreaded subject. The author of this book has used " a friendly approach " to present the stuff so that readers will actively be engaged in learning with less strain. This has not in a sense simplified the difficult elements of Calculus but bringing along the readers to think and reason while studying the subject. It is an Advanced Calculus book which guides the readers to explore and research the myriads of advanced topics. The book is well-organized and will pave way for the much harder topics to be studied and looked up in other references with ease. The text materials are so designed to invoke discovery. For example, in the Green's Theorem section there is Remark 12.7.2 which says, (a) Green's theorem can at times be used to evaluate complicated line integrals by calculating easier iterated integrals. See Exercise 3. (b) A single iterated integral can, perhaps be used to calculate a line integral along a piecewise smooth curve. See Exercise 4. (c) Evaluation of a double integral may be simplified using Green's theorem. See Exercises 5 and 6. (d) Green's theorem can be used to calculate the area of a region just by considering its boundary. See Remark 12.7.3. The exercises are referred to verify the use of Green's theorem.
13 of 13 people found the following review helpful:
5.0 out of 5 stars
This is indeed a FRIENDLY introduction of advanced calculus.,
By "yin_luo" (Toronto, ON CANADA) - See all my reviews
This review is from: Advanced Calculus: A Friendly Approach (Hardcover)
This is an extremely readable book on advanced calculus. This is one of the best math textbooks I have ever seen, concise, clear, and rigorous. You should be able to finish this book with only background in Calculus I & II (and hopefully III). A very good introduction on advanced calculus including vector calculus is provided in this book. This might not be sufficient for a course in analysis, however. For future reading, I would highly recommend Rudin's Principles of Mathematical Analysis.
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