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Symmetry analysis of differential equations : an introduction / Daniel J. Arrigo
Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Verlag: Hoboken, NJ : Wiley, 2015Beschreibung: XIII, 176 SISBN:- 9781118721445
- 9781118721650
- 9781322593203
- 1118721403
- 515.353
- 515/.353 23
- QA387
- QA371
Inhalte:
Zusammenfassung: 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 methodsSymmetry 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. DANIEL J. ARRIGO, PhD, is Professor in the Department of Mathematics at the University of Central Arkansas. The author of over 30 journal articles, his research interests include the construction of exact solutions of PDEs; symmetry analysis of nonlinear PDEs; and solutions to physically important equations, such as nonlinear heat equations and governing equations modeling of granular materials and nonlinear elasticity. In 2008, Dr. Arrigo received the Oklahoma-Arkansas Section of the Mathematical Association of America’s Award for Distinguished Teaching of College or University Mathematics.PPN: PPN: 1657477940Package identifier: Produktsigel: ZDB-30-PAD | ZDB-30-PQE
Cover; Title Page; Copyright; Dedication; Preface; References; Acknowledgments; Chapter 1: An Introduction; 1.1 What Is a Symmetry?; 1.2 Lie Groups; 1.3 Invariance of Differential Equations; 1.4 Some Ordinary Differential Equations; Chapter 2: Ordinary Differential Equations; 2.1 Infinitesimal Transformations; 2.2 Lie's Invariance Condition; 2.3 Standard Integration Techniques; 2.4 Infinitesimal Operator and Higher Order Equations; 2.5 Second-Order Equations; Exercises; 2.6 Higher Order Equations; 2.7 ODE Systems; Chapter 3: Partial Differential Equations; 3.1 First-Order Equations
3.2 Second-Order PDEs3.3 Higher Order PDEs; 3.4 Systems of PDEs; 3.5 Higher Dimensional PDEs; Chapter 4: Nonclassical Symmetries and Compatibility; 4.1 Nonclassical Symmetries; 4.2 Nonclassical Symmetry Analysis and Compatibility; 4.3 Beyond Symmetries Analysis-General Compatibility; 4.4 Concluding Remarks; Solutions; Section 1.5; Section 2.2.1; Section 2.3.6; Section 2.5.1; Section 2.6.1; Section 2.7.3; Section 3.1.4; Section 3.2.5; Section 3.3.1; Section 3.4.3; Section 3.5.1; Section 4.4; References; Index; End User License Agreement
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