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

Watson Fulks is the author of Advanced Calculus: An Introduction to Analysis, 3rd Edition, published by Wiley. 

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