Calculus

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Except "Suggested Reading", I think there is almost no difference between 3rd edition and 4th edition. This book makes you go from struggling in abstraction to realizing that the whole field is intuitive and useful.

As a general thing - it's been a long time since I read this textbook but I have good memories of it. with small Roman numerals, while small letters are used to label interrelated parts in other problems.This arrangement corresponds to the traditional organization of most calculus courses, but I feel that it will only diminish the value of the book for students who have seen a small amount of calculus previously, and for bright students with a reasonable background.

I feel, for a serious mathematician, it is first-year level at best, though a reasonably bright and motivated high school student can easily get through the chapters, if not solve the exercises to utmost completion. About half of this course was devoted to algebra and topology, while the other half covered calculus, with the preliminary edition as the text. This is always safe— after all, the class is unlikely to rise up in a body and protest publicly—but the students themselves, it seems to me, deserve the right to assign credit for the thor­ oughness with which they absorbed an impressive amount of mathematics.Regarding its frequent recommendation to beginning Calculus students, it is far from an ideal book to learn from.

The proof of this assertion involves nothing more than subtracting a from both sides of the equation, in other words, adding —a to both sides; as the following detailed proof shows, all three properties P1-P3 must be used to justify this operation. It is then possible to find the solution of certain simple equations by a series of steps (each justified by Pl, P2, or P3) similar to the ones just presented for the equation a + x = a. A poor condition book can still make a good reading copy but is generally not collectible unless the item is very scarce. Needles to say, they are not responsible for the deficiencies which remain, especially since I sometimes rejected suggestions which would have made the book appear suitable for a larger group of students.

There are now separate Appendices for many topics that were previously slighted: polar coordinates, uniform continuity, parameterized curves, Riemann sums, and the use of integrals for evaluating lengths, volumes and surface areas. Since the most exciting concepts of calculus do not appear until Part III, it should be pointed out that Parts I and II will probably require less time than their length suggests—although the entire book covers a one-year course, the chapters are not meant to be covered at any uniform rate.