Where do solutions go, and how do they behave en route? These are two of the major questions addressed by the qualita- tive theory of differential equations. The purpose of this book is to answer these questions for certain classes of equa- tions by recourse to the framework of semidynamical systems (or topological dynamics as it is sometimes called). This approach makes it possible to treat a seemingly broad range of equations from nonautonomous ordinary differential equa- tions and partial differential equations to stochastic differ- ential equations. The methods are not limited to the...
Where do solutions go, and how do they behave en route? These are two of the major questions addressed by the qualita- tive theory of differential equ...
Stratified fluids whose densities, sound speeds and other parameters are functions of a single depth coordinate occur widely in nature. Indeed, the earth's gravitational field imposes a stratification on its atmosphere, oceans and lakes. It is well known that their stratification has a profound effect on the propagation of sound in these fluids. The most striking effect is probably the occurrence of acoustic ducts, due to minima of the sound speed, that can trap sound waves and cause them to propagate hori- zontally. The reflection, transmission and distortion of sonar signals by acoustic...
Stratified fluids whose densities, sound speeds and other parameters are functions of a single depth coordinate occur widely in nature. Indeed, the ea...
The theory of Boolean algebras was created in 1847 by the English mat- matician George Boole. He conceived it as a calculus (or arithmetic) suitable for a mathematical analysis of logic. The form of his calculus was rather di?erent from the modern version, which came into being during the - riod 1864-1895 through the contributions of William Stanley Jevons, Aug- tus De Morgan, Charles Sanders Peirce, and Ernst Schr] oder. A foundation of the calculus as an abstract algebraic discipline, axiomatized by a set of equations, and admitting many di?erent interpretations, was carried out by Edward...
The theory of Boolean algebras was created in 1847 by the English mat- matician George Boole. He conceived it as a calculus (or arithmetic) suitable f...
Alaska's great size is mirrored by the large number and diversity of its freshwater ecosystems. This volume reviews and synthesizes research on a variety of Alaskan freshwaters including lakes, rivers and wetlands. The vast range of Alaskan habitats ensures that the chapters in this book will provide valuable information for readers interested in freshwaters, particularly nutrient dynamics, biotic adaptations, recovery mechanisms of aquatic biota, stream succession and the management of human-induced changes in aquatic habitats.
Alaska's great size is mirrored by the large number and diversity of its freshwater ecosystems. This volume reviews and synthesizes research on a vari...
Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems.
Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming...
Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve ...
Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been...
Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract ...
This new approach to real analysis stresses the use of the subject with respect to applications, i.e., how the principles and theory of real analysis can be applied in a variety of settings in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization. Users will be prepared for more intensive work in each topic through these applications and their accompanying exercises. This book is appropriate for math enthusiasts with a prior knowledge of both calculus and linear algebra.
This new approach to real analysis stresses the use of the subject with respect to applications, i.e., how the principles and theory of real analys...
Calculus of real-valued functions of several real variables, also known as m- tivariable calculus, is a rich and fascinating subject. On the one hand, it seeks to extend eminently useful and immensely successful notions in one-variable calculus such as limit, continuity, derivative, and integral to "higher dim- sions. " On the other hand, the fact that there is much more room to move n about in the n-space R than on the real line R brings to the fore deeper geometric and topological notions that play a signi?cant role in the study of functions of two or more variables. Courses in...
Calculus of real-valued functions of several real variables, also known as m- tivariable calculus, is a rich and fascinating subject. On the one hand,...
This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and...
This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates...
This is a small book on algebra where the stress is laid on the structure of ?elds, hence its title. Youwillhearaboutequations, bothpolynomialanddi?erential, andabout the algebraic structure of their solutions. For example, it has been known for centuries how to explicitely solve polynomial equations of degree 2 (Baby- nians, many centuries ago), 3 (Scipione del Ferro, Tartaglia, Cardan, around th 1500a.d.), and even 4 (Cardan, Ferrari, xvi century), using only algebraic operations and radicals (nth roots). However, the case of degree 5 remained unsolved until Abel showed in 1826 that a...
This is a small book on algebra where the stress is laid on the structure of ?elds, hence its title. Youwillhearaboutequations, bothpolynomialanddi?er...
