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140122 ||| eng |
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|a 9783642568930
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|a Pahl, Peter J.
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|a Mathematical Foundations of Computational Engineering
|h Elektronische Ressource
|b A Handbook
|c by Peter J. Pahl, Rudolf Damrath
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| 250 |
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|a 1st ed. 2001
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2001, 2001
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| 300 |
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|a XXXVI, 1007 p
|b online resource
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|a Logic -- 1.1 Representation of Thought -- 1.2 Elementary Concepts -- 1.3 Propositional Logic -- 1.4 Predicate Logic -- 1.5 Proofs and Axioms -- Set Theory -- 2.1 Sets -- 2.2 Algebra of Sets -- 2.3 Relations -- 2.4 Types of Relations -- 2.5 Mappings -- 2.6 Types of Mappings -- 2.7 Cardinality and Countability -- 2.8 Structures -- Algebraic Structures -- 3.1 Introduction -- 3.2 Inner Operations -- 3.3 Sets with One Operation -- 3.4 Sets with Two Operations -- 3.5 Vector Spaces -- 3.6 Linear Mappings -- 3.7 Vector and Matrix Algebra -- Ordinal Structures -- 4.1 Introduction -- 4.2 Ordered Sets -- 4.3 Extreme Elements -- 4.4 Ordered Sets with Extremality Properties -- 4.5 Mappings of Ordered Sets -- 4.6 Properties of Ordered Sets -- 4.7 Ordered Cardinal Numbers -- Topological Structures -- 5.1 Introduction -- 5.2 Topological Spaces -- 5.3 Bases and Generating Sets -- 5.4 Metric Spaces -- 5.5 Point Sets in Topological Spaces -- 5.6 Topological Mappings -- 5.7 Construction of Topologies -- 5.8 Connectedness of Sets -- 5.9 Separation Properties -- 5.10 Convergence -- 5.11 Compactness -- 5.12 Continuity of Real Functions -- Number System -- 6.1 Introduction -- 6.2 Natural Numbers -- 6.3 Integers -- 6.4 Rational Numbers -- 6.5 Real Numbers -- 6.6 Complex Numbers -- 6.7 Quaternions -- Groups -- 7.1 Introduction -- 7.2 Groups and Subgroups -- 7.3 Types of Groups -- 7.4 Class Structure -- 7.5 Group Structure -- 7.6 Abelian Groups -- 7.7 Permutations -- 7.8 General Groups -- 7.9 Unique Decomposition of Abelian Groups -- Graphs -- 8.1 Introduction -- 8.2 Algebra of Relations -- 8.3 Classification of Graphs -- 8.4 Structure of Graphs -- 8.5 Paths in Networks -- 8.6 Network Flows -- Tensors -- 9.1 Introduction -- 9.2 Vector Algebra -- 9.3 Tensor Algebra -- 9.4 Tensor Analysis -- Stochastics -- 10.1 Introduction -- 10.2 Random Events -- 10.3 Random Variables -- 10.4 Random Vectors -- 10.5 Random Processes
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| 653 |
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|a Algebraic Topology
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| 653 |
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|a Engineering mathematics
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| 653 |
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|a Computer-Aided Engineering (CAD, CAE) and Design
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| 653 |
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|a Applied Dynamical Systems
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| 653 |
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|a Computational Mathematics and Numerical Analysis
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| 653 |
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|a Mathematics / Data processing
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| 653 |
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|a Computer-aided engineering
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| 653 |
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|a Nonlinear theories
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| 653 |
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|a Civil engineering
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| 653 |
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|a Engineering / Data processing
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| 653 |
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|a Algebraic topology
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| 653 |
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|a Civil Engineering
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| 653 |
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|a Mathematical and Computational Engineering Applications
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| 653 |
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|a Dynamics
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| 700 |
1 |
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|a Damrath, Rudolf
|e [author]
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 028 |
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|a 10.1007/978-3-642-56893-0
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| 856 |
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|u https://doi.org/10.1007/978-3-642-56893-0?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 515.39
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| 520 |
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|a o.Prof. Dr. Dr. h.c. mult. Peter Jan Pahl is an expert in the field of computational engineering, with international activities. He is proposed President of the International Society on Computing in Civil and Structural Engineering. Prof. Dr.-Ing. Rudolf Damrath worked with Professor Pahl for over 20 years and is now international renown himself. They both worked on fundamental topics in computational engineering, especially for numerical applications in civil and structural engineering. This book serves as a comprehensive handbook, bringing the fundamental mathematics of engineering computation into a suitable order for specific engineering purposes, showing their siginificance for typical applications. The relevant definitions, notations and theories are presented in a durable form which is independent of the fast development of information technology
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