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Product Identifiers

PublisherAmerican Mathematical Society

ISBN-100821847910

ISBN-139780821847916

eBay Product ID (ePID)73199288

Product Key Features

Number of Pages590 Pages

Publication NameAdvanced Calculus

LanguageEnglish

Publication Year2009

SubjectCalculus

TypeTextbook

Subject AreaMathematics

AuthorPatrick M. Fitzpatrick

SeriesPure and Applied Undergraduate Texts

FormatHardcover

Dimensions

Item Height1.4 in

Item Weight42.2 Oz

Item Length10.2 in

Item Width7.2 in

Additional Product Features

Edition Number2

Intended AudienceScholarly & Professional

LCCN2008-047395

Dewey Edition22

ReviewsThis is a well-written and well-structured book with clearly explained proofs and a good supply of exercises, some of them are quite challenging. It is this reviewer's opinion that the volume should be an excellent and useful tool for undergraduate students." - Teodora-Liliana Radulescu, Zentralblatt MATH

Series Volume Number5

IllustratedYes

Dewey Decimal515

Table Of ContentPreface Preliminaries 1. Tools for Analysis 2. Convergent Sequences 3. Continuous Functions 4. Differentiation 5. Elementary Functions as Solutions of Differential Equations 6. Integration: Two Fundamental Theorems 7. Integration: Further Topics 8. Approximation by Taylor Polynomials 9. Sequences and Series of Functions 10. The Euclidean Space Rn 11. Continuity, Compactness, and Connectedness 12. Metric Spaces 13. Differentiating Functions of Several Variables 14. Local Approximation of Real-Valued Functions 15. Approximating Nonlinear Mapping by Linear Mappings 16. Images and Inverses: The Inverse Function Theorem 17. The Implicit Function Theorem and its Applications 18. Integrating Functions of Several Variables 19. Iterated Integration and Changes of Variables 20. Line and Surface Integrals Appendix A: Consequences of the Field and Positivity Axioms Appendix B: Linear Algebra Index

Edition DescriptionRevised edition,New Edition

SynopsisAdvanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The 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., Suitable as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis, this book intends to present the fundamental concepts within the context of examples and exercises. It starts with the creation of basic tools using the completeness axiom.

LC Classification NumberQA303.2.F58 2009