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Algorithmic Lie Theory for Solving Ordinary Differential Equations

Fritz Schwarz
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2008
Number of Pages: 
434
Format: 
Hardcover
Series: 
Pure and Applied Mathematics 291
Price: 
89.95
ISBN: 
9781584888895
Category: 
Monograph
We do not plan to review this book.

 INTRODUCTION

LINEAR DIFFERENTIAL EQUATIONS
Linear Ordinary Differential Equations
Janet's Algorithm
Properties of Janet Bases
Solving Partial Differential Equations

LIE TRANSFORMATION GROUPS
Lie Groups and Transformation Groups
Algebraic Properties of Vector Fields
Group Actions in the Plane
Classification of Lie Algebras and Lie Groups
Lie Systems

EQUIVALENCE AND INVARIANTS OF DIFFERENTIAL EQUATIONS
Linear Equations
Nonlinear First-Order Equations
Nonlinear Equations of Second and Higher Order

SYMMETRIES OF DIFFERENTIAL EQUATIONS
Transformation of Differential Equations
Symmetries of First-Order Equations
Symmetries of Second-Order Equations
Symmetries of Nonlinear Third-Order Equations
Symmetries of Linearizable Equations

TRANSFORMATION TO CANONICAL FORM
First-Order Equations
Second-Order Equations
Nonlinear Third-Order Equations
Linearizable Third-Order Equations

SOLUTION ALGORITHMS
First-Order Equations
Second-Order Equations
Nonlinear Equations of Third Order
Linearizable Third-Order Equations

CONCLUDING REMARKS

APPENDIX A: Solutions to Selected Problems
APPENDIX B: Collection of Useful Formulas
APPENDIX C: Algebra of Monomials
APPENDIX D: Loewy Decompositions of Kamke's Collection
APPENDIX E: Symmetries of Kamke's Collection
APPENDIX F: ALLTYPES Userinterface

REFERENCES

INDEX

Dummy View - NOT TO BE DELETED