There exist two essentially different approaches to the study of dynamical systems, based on
the following distinction:
time-continuous nonlinear differential equations ? time-discrete maps
One approach starts from time-continuous differential equations and leads to time-discrete
maps, which are obtained from them by a suitable discretization of time. This path is
pursued, e.g., in the book by Strogatz [Str94]. 1 The other approach starts from the study of
time-discrete maps and then gradually builds up to time-continuous differential equations,
see, e.g., [Ott93, All97, Dev89, Has03, Rob95]. After a short motivation in terms of nonlinear
differential equations, for the rest of this course we shall follow the latter route to dynamical
systems theory. This allows a generally more simple way of introducing the important
concepts, which can usually be carried over to a more complex and physically realistic
CONTEXT.
標簽：
Systems_Rainer
Introduction
Dynamical
Klages
to
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Computer science as an academic discipline began in the 1960’s. Emphasis was on
programming languages, compilers, operating systems, and the mathematical theory that
supported these areas. Courses in theoretical computer science covered finite automata,
regular expressions, CONTEXT-free languages, and computability. In the 1970’s, the study
of algorithms was added as an important component of theory. The emphasis was on
making computers useful. Today, a fundamental change is taking place and the focus is
more on a wealth of applications. There are many reasons for this change. The merging
of computing and communications has played an important role. The enhanced ability
to observe, collect, and store data in the natural sciences, in commerce, and in other
fields calls for a change in our understanding of data and how to handle it in the modern
setting. The emergence of the web and social networks as central aspects of daily life
presents both opportunities and challenges for theory.
標簽：
Foundations
Science
Data
of
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Artificial Intelligence (AI) is a big field, and this is a big book. We have tried to explore the
full breadth of the field, which encompasses logic, probability, and continuous mathematics;
perception, reasoning, learning, and action; and everything from microelectronic devices to
robotic planetary explorers. The book is also big because we go into some depth.
The subtitle of this book is “A Modern Approach.” The intended meaning of this rather
empty phrase is that we have tried to synthesize what is now known into a common frame-
work, rather than trying to explain each subfield of AI in its own historical CONTEXT. We
apologize to those whose subfields are, as a result, less recognizable.
標簽：
A-Modern-Approach
Intelligence
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