In dem Band werden Entstehung und Entwicklung der grundlegenden Begriffe der Analysis von der Antike bis heute ausführlich behandelt. Eingebettet sind diese Informationen in die Beschreibung historischer und kultureller Ereignisse, die Lebensläufe bedeutender Mathematiker und der von ihnen entwickelten Teilgebiete der Analysis. Zahlreiche gezeichnete Figuren veranschaulichen Begriffe, Lehrsätze und Methoden. Jedes Kapitel enthält eine Tabelle mit den Daten der wesentlichen Ergebnisse und Ereignisse aus 3000 Jahren Analysis.
This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.
This title is ´´the´´ essential reference for integrals in the English language. Mathematicians, scientists, and engineers rely on it when identifying and subsequently solving extremely complex problems. The seventh edition includes the most up to date listing of integrals, series, and products and includes a fully searchable CD-ROM.
This book presents the basic concepts of calculus and its relevance to real-world problems, covering the standard topics in their conventional order. By focusing on applications, it allows readers to view mathematics in a practical and relevant setting. Organized into 12 chapters, this book includes numerous interesting, relevant and up-to date applications that are drawn from the fields of business, economics, social and behavioural sciences, life sciences, physical sciences, and other fields of general interest. It also features MATLAB, which is used to solve a number of problems. The book is ideal as a first course in calculus for mathematics and engineering students. It is also useful for students of other sciences who are interested in learning calculus.
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. Drawing on their experiences in teaching, research, and consulting, the authors have produced a textbook that will be of interest to students and practitioners alike. Each chapter begins with the basic concepts and builds up gradually to the best techniques currently available. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. Above all, the authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.For the second edition, the book has been brought up-to-date by adding new topics that have become important since the publication of the first edition, such as the nonlinear interior methods and filter methods. The authors have broadened the scope of the book by including a new chapter on derivative-free methods for optimization, which are used widely in practice and are the focus of much current research. An extensive reorganization and revision of the chapters on unconstrained optimization has been made. Large-scale optimization is treated more extensively. Significant changes have been made to the constrained optimization section. The chapter on theory of constrained optimization was revised and streamlined, and a section on duality added. The linear programming chapters were reorganized and modernized, and contain important new additions concerning dual simplex, presolving, and practical aspects of interior-point methods. New, modern treatments of topics such as sequential quadratic programming, augmented Lagrangian, and barrier methods have been added. Iterative linear algebra techniques in the constrained optimization context are treated more extensively. Lesspractical material (e.g., nonconvex quadratic programming, SQP or equality constraints) was reduced. Finally, many new exercises have been added to existing chapters.
EVERYTHING YOU NEED TO SCORE A PERFECT 5. Ace the AP Calculus BC Exam with this comprehensive study guide-including 3 full-length practice tests, thorough content reviews, targeted strategies for every question type, and access to online extras. Techniques That Actually Work. ? Tried-and-true strategies to avoid traps and beat the test ? Tips for pacing yourself and guessing logically ? Essential tactics to help you work smarter, not harder Everything You Need to Know to Help Achieve a High Score. ? Comprehensive content review for all test topics ? Up-to-date information on the planned 2020 course changes via your online Student Tools ? Engaging activities to help you critically assess your progress ? Access to online drills, study plans, a handy list of formulas, helpful pre-college information, and more Practice Your Way to Excellence. ? 3 full-length practice tests with detailed answer explanations ? Practice drills throughout each content review chapter ? Helpful reference guide of of key calculus formulas and comprehensive drills available online
This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.
EVERYTHING YOU NEED TO SCORE A PERFECT 5. Ace the AP Calculus AB Exam with this comprehensive study guide-including 3 full-length practice tests, content reviews, targeted strategies, and access to online extras including information on the planned College Board course updates coming in 2019-2020. Techniques That Actually Work. ? Tried-and-true strategies to help you avoid traps and beat the test ? Tips for pacing yourself and guessing logically ? Essential tactics to help you work smarter, not harder Everything You Need to Know to Help Achieve a High Score. ? Comprehensive content review for all test topics ? Up-to-date information on the planned 2020 course changes via your online Student Tools ? Subjects organized into manageable units ? Access to online study plans, a handy list of key terms and concepts, helpful pre-college information, and more Practice that Takes You to Excellence. ? 3 full-length practice tests in the book with detailed answer explanations ? Practice drills at the end of each content review chapter ? Handy reference guide of key calculus formulas and comprehensive drill units available online Written by the experts at The Princeton Review, Cracking the AP Calculus AB Exam arms you to take on the test and achieve your highest possible score.
Socio-economic Analysis of Date Palm in Northwestern Nigeria: Olusegun Olusola Obadimu