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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.
1.The Number System
3.Continuity and More Limits
6.The Elementary Transcendental Functions
PART II.VECTOR CALCULUS
7.Vectors and Curves
8.Functions of Several Variables.
Limits and Continuity
10.The Inversion Theorem
12.Line and Surface Integrals
PART III. THEORY OF CONVERGENCE
14.Sequence and Series of Functions.
15.The Taylor Series
17.Integral Representations of Functions
18.Gamma and Beta Functions.Laplace's Method and Stirling's Formula
Watson Fulks is the author of Advanced Calculus: An Introduction to Analysis, 3rd Edition, published by Wiley.
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