Books by Steven G. (Washington University Krantz

This new edition continues the effort to make the book accessible to a broader audience. Many students who take a real analysis course do not have the ideal background. The new edition offers chapters on background material like set theory, logic, and methods of proof. The more advanced material in the book is made more apparent.

This new edition is re-organized to make it more useful and more accessible. The most frequently taught topics are now up front. And the major applications are isolated in their own chapters. This makes this edition the most useable and flexible of any previous editions.

This textbook covers the basics of real analysis for a one- or two-semester course. In a straightforward and concise way, it helps students understand the key ideas and apply the theorems. Each section begins with a boxed introduction that familiarizes students with the upcoming topics and sets the stage for the work to be done. Each chapter generally contains at least 50 exercises that build in difficulty, with an exercise set at the end of every section. This allows students to more easily link the exercises to the material in the section.

Complex Variables: A Physical Approach with Applications, Second Edition offers a notable revision. The emphasis remains on theory and practice. The first part of the text focuses on the fundamental concepts. The author then moves on to a detailed look at how complex variables are used in the real world.

This textbook offers a rare opportunity to teach Lebesgue integration to undergraduates. Focusing on the real line, the author introduces the topic in an accessible way, thus encouraging students to dig into this mainstay of mathematical analysis earlier than the traditional graduate level course.

Designed for a one- or two-semester undergraduate course, this text educates a new generation of mathematical scientists and engineers on differential equations. This edition continues to emphasize examples and mathematical modeling as well as promote analytical thinking to help students in future studies. It improves the exercise sets and examples, reorganizes the material on numerical techniques, and enriches the presentation of predator-prey problems. It also updates the material on nonlinear differential equations and dynamical systems and includes a new appendix that reviews linear algebra.

This textbook covers the basics of real analysis for a one- or two-semester course. In a straightforward and concise way, it helps students understand the key ideas and apply the theorems. Each section begins with a boxed introduction that familiarizes students with the upcoming topics and sets the stage for the work to be done. Each chapter generally contains at least 50 exercises that build in difficulty, with an exercise set at the end of every section. This allows students to more easily link the exercises to the material in the section.

Provides an introduction to the basics of modern topology. This work presents the traditional concepts of topological space, open and closed sets, separation axioms, and more, along with applications of the ideas in Morse, manifold, homotopy, and homology theories.