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9780821847916

Advanced Calculus

by
  • ISBN13:

    9780821847916

  • ISBN10:

    0821847910

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2009-01-13
  • Publisher: Amer Mathematical Society

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Summary

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

Table of Contents

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
Table of Contents provided by Publisher. All Rights Reserved.

Supplemental Materials

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