Textbook
Advanced Calculus: An Introduction to Analysis, 3rd Edition (Reprint)ISBN: 9780471021957
752 pages
January 2016, ©1978

Description
Introduces analysis, presenting analytical proofs backed by geometric intuition and placing minimum reliance on geometric argument. This edition separates continuity and differentiation and expands coverage of integration to include discontinuous functions. The discussion of differentiation of a vector function of a vector variable has been modernized by defining the derivative to be the Jacobian matrix; and, the general form of the chain rule is given, as is the general form of the implicit transformation theorem.
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Table of Contents
CALCULUS OF ONE VARIABLE.
The Number System.
Functions, Sequences, and Limits.
Continuity and More Limits.
Differentiation.
Integration.
The Elementary Transcendental Functions.
VECTOR CALCULUS.
Vectors and Curves.
Functions of Several Variables.
Limits and Continuity.
Differential Functions.
The Inversion Theorem.
Multiple Integrals.
Line and Surface Integrals.
THEORY OF CONVERGENCE.
Infinite Series.
Sequence and Series of Functions.
Uniform Convergence.
The Taylor Series.
Improper Integrals.
Integral Representations of Functions.
Gamma and Beta Functions.
Laplace's Method and Stirling's Formula.
Fourier Series.
Elementary Differentiation and Integration Formulas.
Answers, Hints, and Solutions.
Index.
The Number System.
Functions, Sequences, and Limits.
Continuity and More Limits.
Differentiation.
Integration.
The Elementary Transcendental Functions.
VECTOR CALCULUS.
Vectors and Curves.
Functions of Several Variables.
Limits and Continuity.
Differential Functions.
The Inversion Theorem.
Multiple Integrals.
Line and Surface Integrals.
THEORY OF CONVERGENCE.
Infinite Series.
Sequence and Series of Functions.
Uniform Convergence.
The Taylor Series.
Improper Integrals.
Integral Representations of Functions.
Gamma and Beta Functions.
Laplace's Method and Stirling's Formula.
Fourier Series.
Elementary Differentiation and Integration Formulas.
Answers, Hints, and Solutions.
Index.
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