ISBN13: 978-0534376031

ISBN10: 0534376037

**Summary: ** ADVANCED CALCULUS rigorously presents the fundamental concepts of mathematical analysis in the clearest, simplest way, within the context of illuminating examples and stimulating exercises. Emphasizing the unity of the subject, the text shows that mathematical analysis is not a collection of isolated facts and techniques, but rather a coherent body of knowledge. Beyond the intrinsic importance of the actual subject, the author demonstrates that the study of mathemati ...show morecal analysis instills habits of thought that are essential for a proper understanding of many areas of pure and applied mathematics. Students gain a precise understanding of the subject, together with an appreciation of its coherence and significance. The full book is suitable for a year-long course; the first nine chapters are suitable for a one-term course on functions of a single variable. This book is included in the Brooks/Cole Series in Advanced Mathematics.

Benefits:

- NEW! Many changes, some small and some large, have been made in the proofs to emphasize even more strongly the following point of view: Mathematics students must learn to read mathematics, not just listen to it in class, and this book gives them an opportunity to do so. This is a course for students who are learning the art of proof. When the students read a proof, they should feel they understand how mathematicians discovered the proof and so the text avoids 'rabbit out of the hat' proofs. The proofs seem natural to the students and encourage them to believe they could have discovered the proofs.
- NEW! There has been a fundamental conceptual clarification in the development of the material on the structure of the real numbers and the integral.
- NEW! Many new exercises, of varying degrees of difficulty, have been added. A Solutions Manual is available with detailed solutions to selected problems.
- NEW! A number of non-essential concepts have been eliminated and optional material has been placed in a way to make it possible to cover the essential material more easily and fluidly.
- The text's presentation is conversational and mathematically precise.
- In addition to the essential topics, the author includes important topics such as the approximation methods for estimating integrals, the Weierstrass Approximation Theorem, and metric spaces, without disturbing the coherence of the course.
- A wide variety of exercises helps students gain a genuine understanding of the material. The more challenging problems often stimulate the student to carefully reread the relevant sections in order to properly assimilate the material.

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Brand new. We distribute directly for the publisher. Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. T ...show morehe goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables.Special attention has been paid to the motivation for proofs. Selected topics, such as the Picard Existence Theorem for differential equations, have been included in such a way that selections may be made while preserving a fluid presentation of the essential material.Supplemented with numerous exercises, Advanced Calculus is a perfect book for undergraduate students of analysis. ...show less

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