Mathematical analysis (Massachusetts: Addison-Wesley Publishing Company, 1974)
A glance at the table of contents will reveal that this textbook treats topics inanalysis at the "Advanced Calculus" level. The aim has been to provide a development of the subject which is honest, rigorous, up to date, and, at the same time,not too pedantic. The book provides a transition from elementary calculustoadvanced courses in real and complex function theory, and it introducesthe readerto some of the abstract thinking that pervades modern analysis. The second edition differs from the first in many respects. Point set topology is developed in the setting of general metric spaces as well as in Euclidean n-space,and two new chapters have been added on Lebesgue integration. The material online integrals, vector analysis, and surface integrals has been deleted. The order of some chapters has been rearranged, many sections have been completely rewritten, and several new exercises have been added.
The real and complex number systems -- Some basic notions of set theory -- Elements of point set topology -- Limits and continuity -- Derivatives -- Functions of bounded variation and rectifiable curves -- The riemann-stieltjes integral -- Infinite series and infinite products -- Sequences of functions -- The lebesgue integral -- Fourier series and Fourier integrals -- Multivariable differential calculus -- Implicit functions and extremum problems -- Multiple riemann integrals -- Multiple lebesgue integrals -- Cauchy's theorem and the residue calculus
Includes bibliography and index