Single Variable Calculus Multivariable Calculus Differential Equations Fundamentals of Mathematics Analysis Ordered Sets

 Link to Wiley's site for the book (order can be placed there). Videos. Google books link. This text introduces the reader to the concept of mathematical proofs by constructing the familiar number systems from the axioms of set theory. By taking the axiomatic approach, the typical insecurity what is allowed to be used is avoided: Only what we have already proved can be used. Together with this classical approach to introducing proofs, the text seamlessly integrates current applications, such as digital circuits and public key encryption, as well as proofs for many results we recall from high school, such as divisibility tests and the quadratic formula. Beyond the construction of the number systems, which ultimately was driven by the desire to solve higher order equations, the solution methods for third and fourth order methods are presented, as well as, in a separate chapter, why there can be no such method for fifth and higher order equations. A chapter on the Axiom of Choice, For each section, a video presentation is available.

 Link to Wiley's site for the book (order can be placed there). Videos. Google books link. A concise introduction to fundamental solution methods for ordinary differential equations. Topics include first order equations, constant coefficient equations, Laplace transforms, partial differential equations, series solutions, systems, and numerical methods. The text seamlessly connects to applications (oscillating systems, circuits, heat equation, hydrogen atom) and is written from the point-of-view that reading is an active task. Introductory and practice activities are designed to first prepare the reader for a topic and then to practice after the solution method is understood. For many of the topics, a video presentation is available.

Instructor's guide (pdf).

 Mathematical Analysis - A Concise Introduction (Published by J. Wiley and Sons) This text gives a concise introduction to the analysis of functions of one real variable (continuity, differentiation, Riemann and Lebesgue integration) in part I, an introduction to measure spaces, metric spaces, normed spaces, manifolds and Hilbert spaces in part II and an outlook toward applications (including the finite element method) in part III.

 Instructor's manual (pdf). Single Variable Calculus with Precalculus(Published by Fountainhead Press) This text presents the calculus of functions of one variable, starting seamlessly with precalculus. Special attention is given to the language of mathematics (logic), connections to concurrent science and engineering classes and the students' preparation for multivariable calculus.   Electronic book available at Fountainhead Press

 Table of contents, MV+DE (pdf) Multivariable Calculus(Published by Fountainhead Press)This text concludes the calculus sequence. Substantial connections to the sciences and engineering are presented and used to place the mathematics into a realistic context.   Electronic book available at Fountainhead Press

 Introduction, Table of Contents, Chapter 1 (locked pdf) Link to Birkhäuser's site for the book (order can be placed there) Ordered Sets - An Introduction(Published with Birkhäuser.) This text introduces the reader to the main constructions and ideas in the theory of ordered sets. The theme-based approach presents all constructions in a natural context and allows the reader to confront each new concept in a familiar setting. A multitude of exercises provides training. Open research problems are stated at the end of practically every chapter. These problems are understandable and possibly even solvable with the tools introduced in the respective chapter.Since there are few prerequisites, the text can be used as a focused follow-up or companion to a first proof class (set theory and relations) or to a graph theory class. After covering a comparatively lean core, the text can be used to concentrate on topics such as, for example,structure theory, enumeration or algorithmic aspects. In each of these topics the text lays a solid foundation upon which research in the area can be started by a mathematically mature reader.Aside from introducing open problems that have served and will continue to serve as inspiration for research in ordered sets, the text covers some important topics less customary to discrete mathematics/graph theory.Among these topics are, for example an efficient introduction of homology for graphs and the presentation of forward checking as a more efficient alternative to the standard backtracking algorithm. These topicsas well as the many fundamental results presented give the text lasting value as a reference.