Mathematical Tools for Changing Scale in the Analysis of Physical Systems

1. Auflage 1993
ISBN: 978-0-8493-8934-4
Verlag: Taylor & Francis

Buch, Englisch, 256 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 680 g

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.

Zielgruppe

Professional

Autoren/Hrsg.

Gray, William G.

Leijnse, Anton

Kolar, Randall L.

Blain, Cheryl A.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Experimentalphysik

Inhaltsverzeichnis

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

Über Autor(innen)

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