Calculus

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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. In addition to devel­ oping the students’ intuition about the beautiful concepts of analysis, it is surely equally important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions. Web icon An illustration of a computer application window Wayback Machine Texts icon An illustration of an open book. The equality of (2) and (3) is a direct consequence of P1, although this may not be apparent at first sight (one must let b 4- c play the role of b in Pl, and d the role of c). Derivatives and Integrals 9 Derivatives 149 10 Differentiation 168 11 Significance of the Derivative 188 Appendix.

Every aspect of this book was influenced by the desire to present calculus not merely as a prelude to but as the first real encounter with mathematics. 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 have had time to make only a few changes to the Suggested Reading, which after all these years probably requires a complete revision; this will have to wait until the next edition, which I hope to make in a more timely fashion. The reason for this is suggested by the final item of the reading list: where the author suggests that one could learn as much from all of the other items on the reading list by simply reading the “Oeuvres complètes de Niels Henrik Abel”, Abel being the same mathematician who lends his name to the 'Nobel' in mathematics, the Abel Prize. It also includes challenging exercises and proofs to help students develop critical thinking skills. Polar Coordinates 84 Limits 90 Continuous Functions 115 Three Hard Theorems 122 Least Upper Bounds 133 Appendix. In fact, this short chapter is simply an explanation of what is meant by the “basic properties of numbers,” all of which—addition and multiplication, subtraction and division, solutions of equations and inequalities, factoring and other algebraic manipulations—are already familiar to us.

If anyone has it or knows where I can download it from it would be much appreciated if you can help!

It is a good book for interesting problems, however this treatment will not make you any more successful in a Calculus course, perhaps the opposite since you are likely to be in a course that treats Calculus in a different way. Ideal for honours students and mathematics majors seeking an alternative to doorstop textbooks and more formidable introductions to real analysis.

A poor condition book can still make a good reading copy but is generally not collectible unless the item is very scarce. I expect to solve a good amount of hard calculus problems so I would choose whichever has more problems. There are also various resources available to supplement the textbook, such as solution manuals, study guides, and online resources.It is known for its rigorous and concise approach to the subject, focusing on developing a strong theoretical understanding rather than just teaching problem-solving techniques. 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.

Considerable attention is paid to motivating the discussion, showing why each result is important (though mainly in the pure mathematics context, applications of calculus being mainly found in the problems at the end of each chapter).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.