This extensively classroom-tested book provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. It includes clear proofs, detailed examples, and numerous exercises. The text progresses from single variable to multivariable functions, providing a logical development of material that makes the book suitable for one- and two-semester courses and prepares students for more advanced analysis-based courses. Relevant results from elementary set theory and linear algebra are summarized in the appendices.

Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics. His research interests include functional analysis, semigroups, and probability.

Functions of One Variable: The Real Number System. Numerical Sequences. Limits and Continuity on R. Differentiation on R. Riemann Integration on R. Numerical Infinite Series. Sequences and Series of Functions. Functions of Several Variables: Metric Spaces. Differentiation on Rn. Lebesgue Measure on Rn. Lebesgue Integration on Rn. Curves and Surfaces in Rn. Integration on Surfaces. Appendices. Bibliography. Index.