Advanced Calculus

Advanced Calculus

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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 IndexThe 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.

Title:Advanced Calculus
Author:Patrick Fitzpatrick
Publisher:American Mathematical Soc. - 2006


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