Advanced Calculus

by Fitzpatrick, Patrick M.

• ISBN13: 9780821847916
• ISBN10: 0821847910
• Edition: 2nd
• Format: Hardcover
• Copyright: 2009-01-13
• Publisher: Amer Mathematical Society

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

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