Mathematical Tools for Changing Scale in the Analysis of Physical Systems: 1st Edition (Hardback) book cover

Mathematical Tools for Changing Scale in the Analysis of Physical Systems

1st Edition

By William G. Gray, Anton Leijnse, Randall L. Kolar, Cheryl A. Blain

CRC Press

256 pages

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Hardback: 9780849389344
pub: 1993-07-06
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Description

Mathematical Tools for Changing Scale in the Analysis of Physical Systems presents a new systematic approach to changing the spatial scale of the differential equations describing science and engineering problems. It defines vectors, tensors, and differential operators in arbitrary orthogonal coordinate systems without resorting to conceptually difficult Riemmann-Christoffel tensor and contravariant and covariant base vectors. It reveals the usefulness of generalized functions for indicating curvilineal, surficial, or spatial regions of integration and for transforming among these integration regions. These powerful mathematical tools are harnessed to provide 128 theorems in tabular format (most not previously available in the literature) that transform time-derivative and del operators of a function at one scale to the corresponding operators acting on the function at a larger scale.

Mathematical Tools for Changing Scale in the Analysis of Physical Systems also provides sample applications of the theorems to obtain continuum balance relations for arbitrary surfaces, multiphase systems, and problems of reduced dimensionality. The mathematical techniques and tabulated theorems ensure the book will be an invaluable analysis tool for practitioners and researchers studying balance equations for systems encountered in the fields of hydraulics, hydrology, porous media physics, structural analysis, chemical transport, heat transfer, and continuum mechanics.

Table of Contents

Scope and Basic Concepts

Mathematical Preliminaries

Basic Concepts for Generalized Functions

Integration Scales and Coordinate Systems

Theorem Notation

Applications of Generalized Functions

Integration Theorems

Averaging Theorems

Applications

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied