This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems.

During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms. ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software.

This book describes the development and design of a unique combined data and power management infrastructure for small satellites. This new edition became necessary because in the frame of the system's impressive evolution from an academic prototype to one of today's most advanced core avionics, many elements were upgraded to their next technology generation and diverse new components complement the upgraded design. All elements are presented in updated respectively new chapters.

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Overview of Book This book evolved over a period of years as the authors taught classes in var- tional calculus and applied functional analysis to graduatestudents in engineering and mathematics. The book has likewise been in?uenced by the authors’ research programs that have relied on the application of functional analytic principles to problems in variational calculus, mechanics and control theory. One of the most di?cult tasks in preparing to utilize functional, convex, and set-valued analysis in practical problems in engineering and physics is the inti- dating number of de?nitions, lemmas, theorems and propositions that constitute thefoundationsoffunctionalanalysis. Itcannotbeoveremphasizedthatfunctional analysis can be a powerful tool for analyzing practical problems in mechanics and physics. However, many academicians and researchers spend their lifetime stu- ing abstract mathematics. It is a demanding ?eld that requires discipline and devotion. It is a trite analogy that mathematics can be viewed as a pyramid of knowledge, that builds layer upon layer as more mathematical structure is put in place. The di?culty lies in the fact that an engineer or scientist typically would like to start somewhere “above the base” of the pyramid. Engineers and scientists are not as concerned, generally speaking, with the subtleties of deriving theorems axiomatically. Rather, they are interested in gaining a working knowledge of the applicability of the theory to their ?eld of interest.

Computational Mechanics of Composite Materials lays stress on the advantages of combining theoretical advancements in applied mathematics and mechanics with the probabilistic approach to experimental data in meeting the practical needs of engineers.

Mathematical Physiology provides an introduction into physiology using the tools and perspectives of mathematical modeling and analysis. It describes ways in which mathematical theory may be used to give insights into physiological questions and how physiological questions can in turn lead to new mathematical problems.

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