Advanced Calculus: A Friendly Approach

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Summary: Great Adv Calc Book!
Review: 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.

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Summary: Good introduction to Advanced Calculus / Real analysis
Review: This book contains most of the material you need to know, and is very detailed and "Friendly" !

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Summary: This is indeed a FRIENDLY introduction of advanced calculus.
Review: 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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Summary: A perfect place to start...
Review: 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.

Rating:
Summary: Great Adv Calc Book!
Review: Very readable, with good exercise sets and answers/hints in the back of the book. Of all the books I surveyed, including Apostol's, I would recommend this book as "the one" to be used as either the text for a course, or as a companion book to gain newer/more perspective on the subject.