UID:
almafu_9958071894502883
Umfang:
1 online resource e (xiii, 203 pages) :
,
diagrams
ISBN:
1-283-52565-8
,
9786613838100
,
0-08-095518-5
Serie:
Mathematics in science and engineering ; v. 11
Inhalt:
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
Anmerkung:
Front Cover; Differential Forms: with Applications to the Physical Sciences; Copyright Page; Contents; Foreword; Preface; Chapter I. Introduction; 1.1. Exterior Differential Forms; 1.2. Comparison with Tensors; Chapter II. Exterior algebra; 2.1. The Space of p-vectors; 2.2. Determinants; 2.3. Exterior Products; 2.4. Linear Transformations; 2.5. Inner Product Spaces; 2.6. Inner Products of p-vectors; 2.7. The Star Operator; 2.8. Problems; Chapter III. The Exterior Derivative; 3.1. Differential Forms; 3.2. Exterior Derivative; 3.3. Mappings; 3.4. Change of Coordinates
,
3.5. An Example from Mechanics; 3.6. Converse of the Poincaré Lemma; 3.7. An Example; 3.8. Further Remarks; 3.9. Problems; Chapter IV. Applications; 4.1. Moving Frames in E3; 4.2. Relation between Orthogonal and Skew-symmetric Matrices; 4.3. The 6-dimensional Frame Space; 4.4. The Laplacian, Orthogonal Coordinates; 4.5. Surfaces; 4.6. Maxwell's Field Equations; 4.7. Problems; Chapter V. Manifolds and Integration; 5.1. Introduction; 5.2. Manifolds; 5.3. Tangent Vectors; 5.4. Differential Forms; 5.5. Euclidean Simplices; 5.6. Chains and Boundaries; 5.7. Integration of Forms; 5.8. Stokes' Theorem
,
5.9. Periods and De Rham's Theorems; 5.10. Surfaces; Some Examples; 5.11. Mappings of Chains; 5.12. Problems; Chapter VI. Applications in Euclidean space; 6.1. Volumes in En; 6.2. Winding Numbers, Degree of a Mapping; 6.3. The Hopf Invariant; 6.4. Linking Numbers, the Gauss Integral, Ampère's Law; Chapter VII. Applications to Differential Equations; 7.1. Potential Theory; 7.2. The Heat Equation; 7.3. The Frobenius Integration Theorem; 7.4. Applications of the Frobenius Theorem; 7.5. Systems of Ordinary Equations; 7.6. The Third Lie Theorem; Chapter VIII. Applications to Differential Geometry
,
8.1. Surfaces (Continued); 8.2. Hypersurfaces; 8.3. Riemannian Geometry, Local Theory; 8.4. Riemannian Geometry, Harmonic Integrals; 8.5. Affine Connection; 8.6. Problems; Chapter IX. Applications to Group Theory; 9.1. Lie Groups; 9.2. Examples of Lie Groups; 9.3. Matrix Groups; 9.4. Examples of Matrix Groups; 9.5. Bi-invariant Forms; 9.6. Problems; Chapter X. Applications to Physics; 10.1. Phase and State Space; 10.2. Hamiltonian Systems; 10.3. Integral-invariants; 10.4. Brackets; 10.5. Contact Transformations; 10.6. Fluid Mechanics; 10.7. Problems; BIBLIOGRAPHY; GLOSSARY OF NOTATION; INDEX
,
English
Weitere Ausg.:
ISBN 0-12-259650-1
Sprache:
Englisch
