Advanced Calculus

Inbunden, Engelska, 2009

Del i serien Pure and Applied Undergraduate Texts

1 115 kr

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Beskrivning

Advanced 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.

Produktinformation

Utgivningsdatum:2009-02-28
Mått:182 x 259 x 35 mm
Vikt:1 195 g
Format:Inbunden
Språk:Engelska
Serie:Pure and Applied Undergraduate Texts
Antal sidor:590
Upplaga:2
Förlag:American Mathematical Society
ISBN:9780821847916

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Patrick M. Fitzpatrick, University of Maryland, College Park, MD, USA

Recensioner i media

This 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

Innehållsförteckning

PrefacePreliminaries1. Tools for Analysis2. Convergent Sequences3. Continuous Functions4. Differentiation5. Elementary Functions as Solutions of Differential Equations6. Integration: Two Fundamental Theorems7. Integration: Further Topics8. Approximation by Taylor Polynomials9. Sequences and Series of Functions10. The Euclidean Space Rn11. Continuity, Compactness, and Connectedness12. Metric Spaces13. Differentiating Functions of Several Variables14. Local Approximation of Real-Valued Functions15. Approximating Nonlinear Mapping by Linear Mappings16. Images and Inverses: The Inverse Function Theorem17. The Implicit Function Theorem and its Applications18. Integrating Functions of Several Variables19. Iterated Integration and Changes of Variables20. Line and Surface IntegralsAppendix A: Consequences of the Field and Positivity AxiomsAppendix B: Linear AlgebraIndex