الصفحة 1
الصفحة 1
Introduction to Numerical Methods in Differential Equations
This is a textbook for upper division undergraduates and beginning graduate students. Its objective is that students learn to derive, test and analyze numerical methods for solving differential equations, and this includes both ordinary and partial differential equations. In this sense the book is constructive rather than theoretical, with the intention that the students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. An essential component of this is the exercises, which develop both the analytical and computational aspects of the material. The importance of the subject of the book is that most laws of physics involve differential equations, as do the modern theories on financial assets.
Information and its role in nature
Infromation and Its Role in Nature presents an in-depth interdisciplinary discussion of the concept of information and its role in the control of natural processes. After a brief review of classical and quantum information theory, the author addresses numerous central questions, including: Is information reducible to the laws of physics and chemistry? Does the Universe, in its evolution, constantly generate new information? Or are information and information-processing exclusive attributes of living systems, related to the very definition of life? If so, what is the role of information in classical and quantum physics? In what ways does information-processing in the human brain bring about self-consciousness? Accessible to graduate students and professionals from all scientific disciplines, this stimulating book will help to shed light on many controversial issues at the heart of modern science.
Gravity, Black Holes, and the Very Early Universe : An Introduction to General Relativity and Cosmology
In the early 1900s, Albert Einstein formulated two theories that would forever change the landscape of physics: the Special Theory of Relativity and the General Theory of Relativity. By 1925, quantum mechanics had been born out of the dissection of these two theories, and shortly after that, relativistic quantum field theory. We now had in place some important ties between the laws of physics and the types of particle interactions the new physics was uncovering. Gravity is one of the four types of forces that are found throughout the universe. In fact, although it is a relatively weak force, it operates at huge distances, and so must be accounted for in any cosmological system. Unfortunately, gravity continues to defy our neat categorization of how all the forces in nature work together.
Food Materials Science : Principles and Practice
Food manufacture is about producing billions of units of standardized products which must be cheap, nutritious, safe and appealing to the consumer’s taste. Food products are complex multicomponent and structured edible materials that nevertheless must comply with the laws of physics and fundamentals of engineering sciences. In the last 20 years the design of food products with specific functionalities has advanced significantly by the application of scientific knowledge from disciplines such as polymer physics, colloidal and mesoscopic physics, materials science and new imaging and probing techniques borrowed from chemistry, biology and medicine. Our knowledge of the relationship between microstructure, processing, and macroscopic properties continues to increase as the science of food materials advances at a fast pace.
Linear Systems Control : Deterministic and Stochastic Methods
Modern control theory and in particular state space or state variable methods can be adapted to the description of many different systems because it depends strongly on physical modeling and physical intuition. The laws of physics are in the form of differential equations and for this reason, this book concentrates on system descriptions in this form. This means coupled systems of linear or nonlinear differential equations. The physical approach is emphasized in this book because it is most natural for complex systems. It also makes what would ordinarily be a difficult mathematical subject into one which can straightforwardly be understood intuitively and which deals with concepts which engineering and science students are already familiar.
Laws of Nature
The book is concerned with the laws of nature and in particular with the laws of physics. The authors discuss three important questions: First, whether the observed regularities are based on strict "laws of nature" that hold rigorously and without any exception. Second, what we call a "law of nature" is studied by comparing this concept with invariance principles, causality principles, teleological principles and means of predicting future events. Finally, on the basis of these investigations the authors treat the ambitious and intricate third question, why the laws of nature hold. Are there rational reasons for this largely unexplained phenomenon? This book addresses students as well as researchers. It will be an excellent reference for those interested in the philosophical foundations of the natural sciences.
