Number Systems
The Real Numbers
The Complex Numbers
Sequences
Convergence of Sequences
Subsequences
Limsup and Liminf
Some Special Sequences
Series of Numbers
Convergence of Series
Elementary Convergence Tests
Advanced Convergence Tests
Some Special Series
Operations on Series
Basic Topology
Open and Closed Sets
Further Properties of Open and Closed Sets
Compact Sets
The Cantor Set
Connected and Disconnected Sets
Perfect Sets
Limits and Continuity of Functions
Basic Properties of the Limit of a Function
Continuous Functions
Topological Properties and Continuity
Classifying Discontinuities and Monotonicity
Differentiation of Functions
The Concept of Derivative
The Mean Value Theorem and Applications
More on the Theory of Differentiation
The Integral
Partitions and the Concept of Integral
Properties of the Riemann Integral
Sequences and Series of Functions
Convergence of a Sequence of Functions
More on Uniform Convergence
Series of Functions
The Weierstrass Approximation Theorem
Elementary Transcendental Functions
Power Series
More on Power Series: Convergence Issues
The Exponential and Trigonometric Functions
Logarithms and Powers of Real Numbers
Appendix I: Elementary Number Systems
Appendix II: Logic and Set Theory
Table of Notation
Glossary
Bibliography
Index
Biography
Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has previously taught at UCLA, Princeton University, and Pennsylvania State University. He has written more than 75 books and more than 195 scholarly papers and is the founding editor of the Journal of Geometric Analysis and Complex Analysis and its Synergies. An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D. from Princeton University.
"… there is a good set of exercises in each section … . If real analysis is to be dealt with in a one-semester course, this book appears to provide a reasonable text for the course."
—Mathematical Reviews, April 2015
