Applied Mathematics for Science and Engineering

The final chapter summarizes the results, presents bibliographic comments, and considers future directions in the field.

Employing recent results on elliptic and evolutionary variational inequalities, convex analysis, nonlinear equations with monotone operators, and fixed points of operators, Analysis and Approximation of Contact Problems with Adhesion or Damage places these important tools and results at your fingertips in a unified, accessible reference.

The book focuses on simple two-stage adaptive designs with sample size re-estimation before moving on to explore more challenging designs and issues that include drop-loser, adaptive dose-funding, biomarker-adaptive, multiple-endpoint adaptive, response-adaptive randomization, and Bayesian adaptive designs. In many of the chapters, the author compares methods and provides practical examples of the designs, including those used in oncology, cardiovascular, and inflammation trials.
Equipped with the knowledge of adaptive design presented in this book, you will be able to improve the efficiency of your trial design, thereby reducing the time and cost of drug development.

The timeliness of a manuscript is more than its form, which may be unfinished or tentative. Thus, in some instances, proofs may be merely outlined and results presented which have been or will later be published elsewhere. If possible, a subject index should be included. Publication of Lecture Notes is intended as a service to the international mathematical community, in that a commercial publisher, Springer-Verlag, can offer a wide distribution of documents which would otherwise have a restricted readership. Once published and copyrighted, they can be documented in the scientific literature.

The text models various problem-solving techniques in detail, then provides opportunity to practice these techniques. The text also builds mathematical maturity by emphasizing how to read and write proofs. Many proofs are illustrated with annotated figures and/or motivated by special Discussion sections. The side margins of the text now include “tiny URLs” that direct students to relevant applications, extensions, and computer programs on the textbook website.

The topics here include convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski’s theorem, Riemannian geometry and a method for Dirichlet problems. This monograph, published in English for the first time, gives unparalleled access to a brilliant mind, and advanced students and researchers in applied mathematics and geometry will find it indispensable.