Advanced Calculus: An Introduction to Modern Analysis

An advanced undergraduate textbook, provides mathematics majors, as well as students who need mathematics in their field of study, with an introduction to the theory and applications of elementary analysis. The text presents, in an accessible form, a carefully maintained balance between abstract concepts and applied results of significance that serves to bridge the gap between the two- or three-semester calculus sequence and senior/graduate level courses in the theory and applications of ordinary and partial differential equations, complex variables, numerical methods, and measure and integration theory.

The book focuses on topological concepts, such as compactness, connectedness, and metric spaces, and topics from analysis including Fourier series, numerical analysis, complex integration, generalized functions, and Fourier and Laplace transforms. Applications from genetics, spring systems, enzyme transfer, and a thorough introduction to the classical vibrating string, heat transfer, and brachistochrone problems illustrate this book's usefulness to the non-mathematics major.

Extensive problem sets found throughout the book test the student's understanding of the topics and help develop the student's ability to handle more abstract mathematical ideas. Advanced Calculus: An Introduction to Modern Analysis is intended for junior- and senior-level undergraduate students in mathematics, biology, engineering, physics, and other related disciplines.

An excellent textbook for a one-year course in advanced calculus, the methods employed in this text will increase students' mathematical maturity and prepare them solidly for senior/graduate level topics. The wealth of materials in the text allows the instructor to select topics that are of special interest to the student. A two- or three-semester calculus sequence is required for successful use of this book.