## Mathematical Foundations of Computational Engineering: A HandbookComputational 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 |

### Other editions - View all

Mathematical Foundations of Computational Engineering: A Handbook Peter J. Pahl,Rudolf Damrath Limited preview - 2012 |

### Common terms and phrases

abelian group algebraic structure arbitrary binary relation boolean called cardinal number closed set closure compact complex numbers component connected connectedness contains convergent countable cycle cyclic group defined definition designated direct sum directed graph disjoint divisor domain edge equivalence euclidean Example filter basis finite number flow graph G greatest element group G Hausdorff space Hence homomorphic idempotent identity element implies infinite inner operation integers intersection inverse isomorphic least element linear combination mapping f matrix maximal metric space multiplication natural numbers neighborhood non-empty normal form normal subgroup open initial open set order relation ordered set pair partially ordered path algebra permutation predicate logic preimage Proof properties quotient group quotient set rational numbers real numbers rules Section sequence f simple graph statement subgroup H subset subspace symmetric theorem topological space topology totally ordered underlying set union unique unit element vector space vertex set vertices zero element

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