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9781118721407 English 1118721403 A self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEs"Symmetry Analysis of Differential Equations: An Introduction "presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs). Providing comprehensive coverage, the book fills a gap in the literature by discussing elementary symmetry concepts and invariance, including methods for reducing the complexity of ODEs and PDEs in an effort to solve the associated problems. Thoroughly class-tested, the author presents classical methods in a systematic, logical, and well-balanced manner. As the book progresses, the chapters graduate from elementary symmetries and the invariance of algebraic equations, to ODEs and PDEs, followed by coverage of the nonclassical method and compatibility. "Symmetry Analysis of Differential Equations: An Introduction "also features: Detailed, step-by-step examples to guide readers through the methods of symmetry analysisEnd-of-chapter exercises, varying from elementary to advanced, with select solutions to aid in the calculation of the presented algorithmic methods"Symmetry Analysis of Differential Equations: An Introduction "is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics. The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in solving differential equations., Symmetry analysis has played a crucial role in the construction of exact solutions to differential equations. In fact, all the standard techniques for solving first order ordinary differential equations (ODEs) can be explained by symmetry analysis. The usefulness of symmetry analysis is readily evident, and the beauty of the method is that it is both fairly easy to learn and is very algorithmic, making it amenable to a variety of computer algebra packages such as Maple(tm) or Mathematica�. An Introduction to Symmetry Analysis of Differential Equations fills a gap in the literature by providing introductory coverage of both ODEs and partial differential equations (PDEs), explores select advanced topics, and contains platiful problems with complete solutions. Chapter coverages includes: ordinary differential equations with Lie's invariance condition, standard integration techniques, infinitesimal operator and higher order equations, second order questions, and ODE systems; partial differential equations with first and second order equations, systems of PDEs, higher dimensional PDEs, and nonclassical symmetries; and compatibility with nonclassical symmetry analysis and first order compatibility.
9781118721407 English 1118721403 A self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEs"Symmetry Analysis of Differential Equations: An Introduction "presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs). Providing comprehensive coverage, the book fills a gap in the literature by discussing elementary symmetry concepts and invariance, including methods for reducing the complexity of ODEs and PDEs in an effort to solve the associated problems. Thoroughly class-tested, the author presents classical methods in a systematic, logical, and well-balanced manner. As the book progresses, the chapters graduate from elementary symmetries and the invariance of algebraic equations, to ODEs and PDEs, followed by coverage of the nonclassical method and compatibility. "Symmetry Analysis of Differential Equations: An Introduction "also features: Detailed, step-by-step examples to guide readers through the methods of symmetry analysisEnd-of-chapter exercises, varying from elementary to advanced, with select solutions to aid in the calculation of the presented algorithmic methods"Symmetry Analysis of Differential Equations: An Introduction "is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics. The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in solving differential equations., Symmetry analysis has played a crucial role in the construction of exact solutions to differential equations. In fact, all the standard techniques for solving first order ordinary differential equations (ODEs) can be explained by symmetry analysis. The usefulness of symmetry analysis is readily evident, and the beauty of the method is that it is both fairly easy to learn and is very algorithmic, making it amenable to a variety of computer algebra packages such as Maple(tm) or Mathematica�. An Introduction to Symmetry Analysis of Differential Equations fills a gap in the literature by providing introductory coverage of both ODEs and partial differential equations (PDEs), explores select advanced topics, and contains platiful problems with complete solutions. Chapter coverages includes: ordinary differential equations with Lie's invariance condition, standard integration techniques, infinitesimal operator and higher order equations, second order questions, and ODE systems; partial differential equations with first and second order equations, systems of PDEs, higher dimensional PDEs, and nonclassical symmetries; and compatibility with nonclassical symmetry analysis and first order compatibility.