Advanced Calculus

Name: Advanced Calculus
Availability: InStock
ISBN: 9780821847916

ISBN-10: 0821847910

ISBN-13: 9780821847916

Edition: 2nd 2009 (Revised)

Authors: Patrick M. Fitzpatrick

List price: $93.00

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Description:

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…

Book details

List price: $93.00
Edition: 2nd
Copyright year: 2009
Publisher: American Mathematical Society
Publication date: 2/28/2009
Binding: Hardcover
Pages: 590
Size: 6.25" wide x 9.00" long x 1.00" tall
Weight: 2.794
Language: English



Preliminaries


Tools for analysis


Convergent sequences


Continuous functions Differentiation


Elementary functions as solutions of differential equations


Integration: Two fundamental theorems


Integration: Further topics


Approximation by Taylor polynomials


Sequences and series of functions


The Euclidean space ${\mathbb R}^n$


Continuity, compactness, and connectedness Metric spaces


Differentiating functions of several variables


Local approximation of real-valued functions


Approximating nonlinear mappings by linear mappings


Images and inverses: The inverse function theorem


The implicit function theorem and its applications


Integrating functions of several variables


Iterated integration and changes of variables


Line and surface integrals


Consequences of the field and positivity axioms


Linear algebra


Index