
Hardcover ISBN: | 979-8-9890528-8-2 |
Product Code: | XYZ/57 |
List Price: | $59.95 |
AMS Member Price: | $47.96 |

Hardcover ISBN: | 979-8-9890528-8-2 |
Product Code: | XYZ/57 |
List Price: | $59.95 |
AMS Member Price: | $47.96 |
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Book DetailsXYZ SeriesVolume: 57; 2024; 360 ppMSC: Primary 00; 97
The constructed name "Calculus CD" does not refer to a specific concept, but rather adopts a nominative spirit of progressively increasing difficulty and depth of concepts in calculus. The inspiration behind the book's title originated from a problem that started as “\(\mathrm{ABCD}\ldots\) is a broken line with \(\mathrm{AB} < \mathrm{BC} < \mathrm{CD} < \ldots\)”. It is safe to say that this book presents a more advanced view of calculus than the typical preparatory high school or college courses.
The book is divided into four chapters that are designed to engage readers in the study of calculus. Throughout the chapters, each of the studies is corroborated by many examples, solved problems, and proposed problems. Full and detailed solutions are provided for all problems included in the book.
The first chapter is dedicated to the study of real numbers. In particular, the reader encounters the axioms of real numbers and the notion of rationality versus irrationality, while exploring interesting consequences of the density of the rational numbers. In the second chapter, the focus shifts to sequences of real numbers, examining convergent and divergent sequences, working with limits, and understanding their profound implications. The third chapter explores series and infinite products. Starting with some fundamentals and elementary convergence tests, the concepts of absolute convergence and conditional convergence are showcased. The last chapter proposes a problem set drawn from different areas of mathematics unified by the application of the knowledge acquired in the previous chapters.
A publication of XYZ Press. Distributed in North America by the American Mathematical Society.
ReadershipThe aim of this book is to serve not only as a textbook for students aspiring to master calculus, but also for those participating in undergraduate mathematics competitions, as well as instructors who want to introduce a fresh view of calculus in their math circles.
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The constructed name "Calculus CD" does not refer to a specific concept, but rather adopts a nominative spirit of progressively increasing difficulty and depth of concepts in calculus. The inspiration behind the book's title originated from a problem that started as “\(\mathrm{ABCD}\ldots\) is a broken line with \(\mathrm{AB} < \mathrm{BC} < \mathrm{CD} < \ldots\)”. It is safe to say that this book presents a more advanced view of calculus than the typical preparatory high school or college courses.
The book is divided into four chapters that are designed to engage readers in the study of calculus. Throughout the chapters, each of the studies is corroborated by many examples, solved problems, and proposed problems. Full and detailed solutions are provided for all problems included in the book.
The first chapter is dedicated to the study of real numbers. In particular, the reader encounters the axioms of real numbers and the notion of rationality versus irrationality, while exploring interesting consequences of the density of the rational numbers. In the second chapter, the focus shifts to sequences of real numbers, examining convergent and divergent sequences, working with limits, and understanding their profound implications. The third chapter explores series and infinite products. Starting with some fundamentals and elementary convergence tests, the concepts of absolute convergence and conditional convergence are showcased. The last chapter proposes a problem set drawn from different areas of mathematics unified by the application of the knowledge acquired in the previous chapters.
A publication of XYZ Press. Distributed in North America by the American Mathematical Society.
The aim of this book is to serve not only as a textbook for students aspiring to master calculus, but also for those participating in undergraduate mathematics competitions, as well as instructors who want to introduce a fresh view of calculus in their math circles.