Introduction to Calculus and Classical Analysis (eBook)

Omar Hijab (Autor)

eBook Download: PDF

2007 | 2. Auflage
352 Seiten
Springer New York (Verlag)
978-0-387-69316-3 (ISBN)

Infos

This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. The book contains many remarkable features: - complete avoidance of /epsilon-/delta arguments by instead using sequences, - definition of the integral as the area under the graph, while area is defined for EVERY subset of the plane, - complete avoidance of complex numbers, - heavy emphasis on computational problems, - applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more, - 344 problems with solutions in the back of the book, - interesting applications, many of which are not usually found in advanced calculus books

About the first edition: 'The treatment, however, is far from standard, and many topics are included, especially in the last chapter, that are not available in other modern elementary texts…This is a rigorous book with good motivational material and explanatory remarks. It includes 347 problems, with solutions given in a 73-page appendix…some of the most attractive material requires considerable skill in manipulation.' D.H. Armitage (MathSciNet). New in the second edition: For the new edition, the author has corrected errors and rewritten large portions of the text. In addition, the author has introduced new topics, such as a combinatorial proof that the radius of convergence of the Bernoulli series is 2p. 'ICCA is beautifully conceived and carefully executed...[this book] has much to teach, both about mathematics and how to write mathematics.' Marvin Knopp, American Mathematical Monthly.

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This is the second edition of an undergraduate one-variable analysis text. Apart from correcting errors and rewriting several sections, material has been added, notably in Chapter 1 and Chapter 4. A noteworthy addition is a re- variable computation of the radius of convergence of the Bernoulli series using the root test (Chapter 5). What follows is the preface from the ?rst edition. For undergraduate students, the transition from calculus to analysis is often disorienting and mysterious. What happened to the beautiful calculus formulas?Wheredid -? andopensetscomefrom?Itisnotuntillaterthatone integrates these seemingly distinct points of view. When teaching "e;advanced calculus"e;, I always had a di?cult time answering these questions. Now,everymathematicianknowsthatanalysisarosenaturallyintheni- teenthcenturyoutofthecalculusoftheprevioustwocenturies.Believingthat it was possible to write a book re?ecting, explicitly, this organic growth, I set outtodoso. I chose several of the jewels of classical eighteenth and nineteenth century analysisandinsertedthemattheendofthebook,insertedtheaxiomsforreals at the beginning, and ?lled in the middle with (and only with) the material necessaryforclarityandlogical completeness.Intheprocess,everylittle piece of one-variable calculus assumed its proper place, and theory and application were interwoven throughout.

Produkt-Details

• Erscheint lt. Verlag: 17.4.2007
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• ISBN-10: 0-387-69316-5 / 0387693165
• ISBN-13: 978-0-387-69316-3 / 9780387693163