Includes index.

Bibliography: p. [335]-336.

Machine derived contents note: Chapter 1: The Real and Complex Number Systems -- Introduction -- Ordered Sets -- Fields -- The Real Field -- The Extended Real Number System -- The Complex Field -- Euclidean Spaces -- Appendix -- Exercises -- Chapter 2: Basic Topology -- Finite, Countable, and Uncountable Sets -- Metric Spaces -- Compact Sets -- Perfect Sets -- Connected Sets -- Exercises -- Chapter 3: Numerical Sequences and Series -- Convergent Sequences -- Subsequences -- Cauchy Sequences -- Upper and Lower Limits -- Some Special Sequences -- Series -- Series of Nonnegative Terms -- The Number e -- The Root and Ratio Tests -- Power Series -- Summation by Parts -- Absolute Convergence -- Addition and Multiplication of Series -- Rearrangements -- Exercises -- Chapter 4: Continuity -- Limits of Functions -- Continuous Functions -- Continuity and Compactness -- Continuity and Connectedness -- Discontinuities -- Monotonic Functions -- Infinite Limits and Limits at Infinity -- Exercises -- Chapter 5: Differentiation -- The Derivative of a Real Function -- Mean Value Theorems -- The Continuity of Derivatives -- L'Hospital's Rule -- Derivatives of Higher-Order -- Taylor's Theorem -- Differentiation of Vector-valued Functions -- Exercises -- Chapter 6: The Riemann-Stieltjes Integral -- Definition and Existence of the Integral -- Properties of the Integral -- Integration and Differentiation -- Integration of Vector-valued Functions -- Rectifiable Curves -- Exercises -- Chapter 7: Sequences and Series of Functions -- Discussion of Main Problem -- Uniform Convergence -- Uniform Convergence and Continuity -- Uniform Convergence and Integration -- Uniform Convergence and Differentiation -- Equicontinuous Families of Functions -- The Stone-Weierstrass Theorem -- Exercises -- Chapter 8: Some Special Functions -- Power Series -- The Exponential and Logarithmic Functions -- The Trigonometric Functions -- The Algebraic Completeness of the Complex Field -- Fourier Series -- The Gamma Function -- Exercises -- Chapter 9: Functions of Several Variables -- Linear Transformations -- Differentiation -- The Contraction Principle -- The Inverse Function Theorem -- The Implicit Function Theorem -- The Rank Theorem -- Determinants -- Derivatives of Higher Order -- Differentiation of Integrals -- Exercises -- Chapter 10: Integration of Differential Forms -- Integration -- Primitive Mappings -- Partitions of Unity -- Change of Variables -- Differential Forms -- Simplexes and Chains -- Stokes' Theorem -- Closed Forms and Exact Forms -- Vector Analysis -- Exercises -- Chapter 11: The Lebesgue Theory -- Set Functions -- Construction of the Lebesgue Measure -- Measure Spaces -- Measurable Functions -- Simple Functions -- Integration -- Comparison with the Riemann Integral -- Integration of Complex Functions -- Functions of Class L� -- Exercises -- Bibliography -- List of Special Symbols -- Index.