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Similarity Methods for Differential Equations

Bluman, George W.; Bluman, G. W. and Cole, J. D.

Published by SPRINGER VERLAG GMBH 01/03/2014 (2014)

ISBN 10: 0387901078 ISBN 13: 9780387901077

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Item Description: SPRINGER VERLAG GMBH 01/03/2014, 2014. Paperback. Book Condition: New. New Book. This item is printed on demand. Shipped from US This item is printed on demand. Bookseller Inventory # IH-9780387901077

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Similarity Methods for Differential Equations

G.W. Bluman, J.D. Cole

Published by Springer-Verlag New York Inc., New York, NY (1974)

ISBN 10: 0387901078 ISBN 13: 9780387901077

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Item Description: Springer-Verlag New York Inc., New York, NY, 1974. Book Condition: New. Language: english. Print On Demand. Bookseller Inventory # 7558114

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Similarity Methods for Differential Equations (Paperback)

G.W. Bluman, J.D. Cole

Published by Springer-Verlag New York Inc., United States (1975)

ISBN 10: 0387901078 ISBN 13: 9780387901077

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Item Description: Springer-Verlag New York Inc., United States, 1975. Paperback. Book Condition: New. 244 x 170 mm. Brand New Book ***** Print on Demand *****. The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans- formations. The goal of these methods is the expression of a solution in terms of quadrature in the case of ordinary differential equations of first order and a reduction in order for higher order equations. For partial differential equations at least a reduction in the number of independent variables is sought and in favorable cases a reduction to ordinary differential equations with special solutions or quadrature. In the last century, approximately one hundred years ago, Sophus Lie tried to construct a general integration theory, in the above sense, for ordinary differential equations. Following Abel s approach for algebraic equations he studied the invariance of ordinary differential equations under transformations. In particular, Lie introduced the study of continuous groups of transformations of ordinary differential equations, based on the infinitesimal properties of the group. In a sense the theory was completely successful. It was shown how for a first-order differential equation the knowledge of a group leads immediately to quadrature, and for a higher order equation (or system) to a reduction in order. In another sense this theory is somewhat disappointing in that for a first-order differ- ential equation essentially no systematic way can be given for finding the groups or showing that they do not exist for a first-order differential equation. Softcover reprint of the original 1st ed. 1974. Bookseller Inventory # APC9780387901077

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Similarity Methods for Differential Equations (Paperback)

G.W. Bluman, J.D. Cole

Published by Springer-Verlag New York Inc., United States (1975)

ISBN 10: 0387901078 ISBN 13: 9780387901077

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Quantity Available: 10

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Item Description: Springer-Verlag New York Inc., United States, 1975. Paperback. Book Condition: New. 244 x 170 mm. Brand New Book ***** Print on Demand *****.The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans- formations. The goal of these methods is the expression of a solution in terms of quadrature in the case of ordinary differential equations of first order and a reduction in order for higher order equations. For partial differential equations at least a reduction in the number of independent variables is sought and in favorable cases a reduction to ordinary differential equations with special solutions or quadrature. In the last century, approximately one hundred years ago, Sophus Lie tried to construct a general integration theory, in the above sense, for ordinary differential equations. Following Abel s approach for algebraic equations he studied the invariance of ordinary differential equations under transformations. In particular, Lie introduced the study of continuous groups of transformations of ordinary differential equations, based on the infinitesimal properties of the group. In a sense the theory was completely successful. It was shown how for a first-order differential equation the knowledge of a group leads immediately to quadrature, and for a higher order equation (or system) to a reduction in order. In another sense this theory is somewhat disappointing in that for a first-order differ- ential equation essentially no systematic way can be given for finding the groups or showing that they do not exist for a first-order differential equation. Softcover reprint of the original 1st ed. 1974. Bookseller Inventory # APC9780387901077

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Similarity Methods for Differential Equations

Bluman, George W.; Bluman, G. W. and Cole, J. D.

Published by SPRINGER VERLAG GMBH 01/07/2014 (2014)

ISBN 10: 0387901078 ISBN 13: 9780387901077

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Item Description: SPRINGER VERLAG GMBH 01/07/2014, 2014. Paperback. Book Condition: New. New Book. This item is printed on demand. Shipped from UK. This item is printed on demand. Bookseller Inventory # IQ-9780387901077

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