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Mathematical Foundations of Computational Engineering A Handbook

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 2...

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Bibliographic Details
Main Authors: Pahl, Peter J., Damrath, Rudolf (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2001, 2001
Edition:1st ed. 2001
Subjects:
Algebraic Topology
Engineering Mathematics
Computer-aided Engineering (cad, Cae) And Design
Applied Dynamical Systems
Computational Mathematics And Numerical Analysis
Mathematics / Data Processing
Computer-aided Engineering
Nonlinear Theories
Civil Engineering
Engineering / Data Processing
Mathematical And Computational Engineering Applications
Dynamics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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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