
Differential Forms with Applications to the Physical Sciences by Harley Flanders
- 322 pages
- English
- PDF
- Available on iOS & Android
Differential Forms with Applications to the Physical Sciences by Harley Flanders
About this book
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
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Table of contents
- Front Cover
- Differential Forms: with Applications to the Physical Sciences
- Copyright Page⤀
- Contents
- Foreword
- Preface
- Chapter I. Introduction
- Chapter II. Exterior algebra
- Chapter III. The Exterior Derivative
- Chapter IV. Applications
- Chapter V. Manifolds and Integration
- Chapter VI. Applications in Euclidean space
- Chapter VII. Applications to Differential Equations
- Chapter VIII. Applications to Differential Geometry
- Chapter IX. Applications to Group Theory
- Chapter X. Applications to Physics
- BIBLIOGRAPHY
- GLOSSARY OF NOTATION
- INDEX