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.

PART I. 1.The Number System 2.Functions,Sequences,and Limits 3.Continuity and More Limits 4.Differentiation 5.Integration 6.The Elementary Transcendental Functions PART II.VECTOR CALCULUS 7.Vectors and Curves 8.Functions of Several Variables. Limits and Continuity 9.Differentiable Functions 10.The Inversion Theorem 11.Multiple Integrals 12.Line and Surface Integrals PART III. THEORY OF CONVERGENCE 13.Infinite Series 14.Sequence and Series of Functions. Uniform Convergence 15.The Taylor Series 16.Improper Integrals 17.Integral Representations of Functions 18.Gamma and Beta Functions.Laplace's Method and Stirling's Formula 19.Fourier Series

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