Real Variables with Basic Metric Space Topology

Designed for a first course in real variables this text presents the fundamentals for more advanced mathematical work particularly in the areas of complex variables measure theory differential equations functional analysis and probability. Geared toward advanced undergraduate and graduate students of mathematics it is also appropriate for students of engineering physics and economics who seek an understanding of real analysis.<br>The author encourages an intuitive approach to problem solving and offers concrete examples diagrams and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text making this volume ideal for independent study. Topics include metric spaces Euclidean spaces and their basic topological properties sequences and series of real numbers continuous functions differentiation Riemann-Stieltjes integration and uniform convergence and applications.