Mathematical Foundations of Computational Engineering: A Handbook

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Springer Science & Business Media, Jul 2, 2001 - Computers - 1008 pages
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Computational engineering is the treatment of engineering tasks with computers. It is based on computational mathematics, which is presented here in a comprehensive handbook. Engineers and scientists who deal with engineering tasks have to handle large amounts of information, which must be created and structured in a systematic manner. This demands a high level of abstraction and therefore knowledge of the mathematical foundations. From the existing rich repertoire of mathematical theories and methods, the fundamentals of engineering computation are selected and presented in a coherent fashion. They are brought into a suitable order for specific engineering purposes, and their significance for typical applications is shown. The relevant definitions, notations and theories are presented in a durable form which is independent of the fast development of information and communication technology.
 

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Contents

LOGIC
1
STOCHASTICS
10
SET THEORY
31
ORDINAL STRUCTURES
50
ALGEBRAIC STRUCTURES
59
TOPOLOGICAL STRUCTURES
161
NUMBER SYSTEM
285
GROUPS
309
GRAPHS
489
Index 991
492
TENSORS
671
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About the author (2001)

Peter Jan Pahl is President of the International Society on Computing in Civil and Structural Engineering.