This book is about solving partial differential equations (PDEs). Such equa tions are used to model a wide range ofphenomena in virtually all fields ofsci ence and technology. Inthe last decade, the general availability of extremely powerful computers has shifted the focus in computational mathematics from simplified model problems to much more sophisticated models resembling in tricate features of real life. This change challenges our knowledge in computer science and in numerical analysis. The main objective ofthe present book is to teach modern, advanced tech niques for numerical PDE...
This book is about solving partial differential equations (PDEs). Such equa tions are used to model a wide range ofphenomena in virtually all fields o...
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems,...
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disc...
In diesem Buch werden die Grundlagen partieller Differentialgleichungen sowie mit der Untersuchung numerischer Methoden fur diese partiellen Differentialgleichungen in Zusammenhang stehende wichtige Uberlegungen vorgestellt. Standardthemen wie Trennung der Variablen, Fourier Analysis, Maximumprinzipien und Energieabschatzungen werden behandelt. Numerische Verfahren werden parallel zur klassischen Theorie vorgestellt. Die Eigenschaften von Differentialgleichungen werden anhand numerischer Experimente veranschaulicht, und die Theorie der finiten Differentialapproximationen wird entwickelt....
In diesem Buch werden die Grundlagen partieller Differentialgleichungen sowie mit der Untersuchung numerischer Methoden fur diese partiellen Different...
Aslak Tveito Hans Petter Langtangen Bj Rn Frederik Nielsen
Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will...
Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and tech...
'Challenges in Computing' sheds light on how mathematical models and computing can help understanding and prediction of complicated physical processes; how communication networks should be designed and implemented to meet the increasingly challenging requirements from users; and how modern engineering principles can lead to better and more robust software systems.
'Challenges in Computing' sheds light on how mathematical models and computing can help understanding and prediction of complicated physical processes...
Combining both the classical theory and numerical techniques for partial differential equations, this thoroughly modern approach shows the significance of computations in PDEs and illustrates the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between these techniques. The authors present the material at an easy pace and exercises ranging from the straightforward to the challenging have been included. In addition there are some "projects" suggested, either to refresh the students...
Combining both the classical theory and numerical techniques for partial differential equations, this thoroughly modern approach shows the significanc...
Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various...
Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is ...
This book shows how mathematical models can aid understanding of complicated physical processes; how communication networks can be designed to meet challenging user needs and how modern engineering principles can lead to better, more robust software systems.
This book shows how mathematical models can aid understanding of complicated physical processes; how communication networks can be designed to meet ch...
