{"product_id":"symmetry-analysis-of-differential-equations-9781118721407","title":"Symmetry Analysis of Differential Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEs\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSymmetry Analysis of Differential Equations: An Introduction \u003c\/i\u003epresents 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. \u003cbr\u003e\u003cbr\u003eThoroughly 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. \u003ci\u003eSymmetry Analysis of Differential Equations: An Introduction \u003c\/i\u003eal\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 An Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 What is a Symmetry? 1\u003c\/p\u003e \u003cp\u003e1.2 Lie Groups 4\u003c\/p\u003e \u003cp\u003e1.3 Invariance of Differential Equations 6\u003c\/p\u003e \u003cp\u003e1.4 Some Ordinary Differential Equations 8\u003c\/p\u003e \u003cp\u003eExercises 12\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Ordinary Differential Equations 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Infinitesimal Transformations 19\u003c\/p\u003e \u003cp\u003e2.2 Lie’s Invariance Condition 23\u003c\/p\u003e \u003cp\u003eExercises 27\u003c\/p\u003e \u003cp\u003e2.3 Standard Integration Techniques 28\u003c\/p\u003e \u003cp\u003e2.3.1 Linear Equations 28\u003c\/p\u003e \u003cp\u003e2.3.2 Bernoulli Equation 30\u003c\/p\u003e \u003cp\u003e2.3.3 Homogeneous Equations 31\u003c\/p\u003e \u003cp\u003e2.3.4 Exact Equations 32\u003c\/p\u003e \u003cp\u003e2.3.5 Riccati Equations 35\u003c\/p\u003e \u003cp\u003eExercises 37\u003c\/p\u003e \u003cp\u003e2.4 Infinitesimal Operator and Higher Order Equations 38\u003c\/p\u003e \u003cp\u003e2.4.1 The Infinitesimal Operator 38\u003c\/p\u003e \u003cp\u003e2.4.2 The Extended Operator 39\u003c\/p\u003e \u003cp\u003e2.4.3 Extension to Higher Orders 40\u003c\/p\u003e \u003cp\u003e2.4.4 First-Order Infinitesimals (revisited) 40\u003c\/p\u003e \u003cp\u003e2.4.5 Second-Order Infinitesimals 41\u003c\/p\u003e \u003cp\u003e2.4.6 The Invariance of Second-Order Equations 42\u003c\/p\u003e \u003cp\u003e2.4.7 Equations of arbitrary order 43\u003c\/p\u003e \u003cp\u003e2.5 Second-Order Equations 43\u003c\/p\u003e \u003cp\u003eExercises 55\u003c\/p\u003e \u003cp\u003e2.6 Higher Order Equations 56\u003c\/p\u003e \u003cp\u003eExercises 61\u003c\/p\u003e \u003cp\u003e2.7 ODE Systems 61\u003c\/p\u003e \u003cp\u003e2.7.1 First Order Systems 61\u003c\/p\u003e \u003cp\u003e2.7.2 Higher Order Systems 67\u003c\/p\u003e \u003cp\u003eExercises 71\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Partial Differential Equations 73\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 First-Order Equations 73\u003c\/p\u003e \u003cp\u003e3.1.1 What Do We Do with the Symmetries of PDEs? 77\u003c\/p\u003e \u003cp\u003e3.1.2 Direct Reductions 80\u003c\/p\u003e \u003cp\u003e3.1.3 The Invariant Surface Condition 83\u003c\/p\u003e \u003cp\u003eExercises 84\u003c\/p\u003e \u003cp\u003e3.2 Second-Order PDEs 84\u003c\/p\u003e \u003cp\u003e3.2.1 Heat Equation 84\u003c\/p\u003e \u003cp\u003e3.2.2 Laplace’s Equation 91\u003c\/p\u003e \u003cp\u003e3.2.3 Burgers’ Equation and a Relative 94\u003c\/p\u003e \u003cp\u003e3.2.4 Heat Equation with a Source 100\u003c\/p\u003e \u003cp\u003eExercises 107\u003c\/p\u003e \u003cp\u003e3.3 Higher Order PDEs 109\u003c\/p\u003e \u003cp\u003eExercises 115\u003c\/p\u003e \u003cp\u003e3.4 Systems of PDEs 115\u003c\/p\u003e \u003cp\u003e3.4.1 First-Order Systems 115\u003c\/p\u003e \u003cp\u003e3.4.2 Second-Order Systems 120\u003c\/p\u003e \u003cp\u003eExercises 124\u003c\/p\u003e \u003cp\u003e3.5 Higher Dimensional PDEs 126\u003c\/p\u003e \u003cp\u003eExercises 132\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Nonclassical Symmetries and Compatibility 133\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Nonclassical Symmetries 133\u003c\/p\u003e \u003cp\u003e4.1.1 Invariance of the Invariant Surface Condition 135\u003c\/p\u003e \u003cp\u003e4.1.2 The Nonclassical Method 137\u003c\/p\u003e \u003cp\u003e4.2 Nonclassical Symmetry Analysis and Compatibility 146\u003c\/p\u003e \u003cp\u003e4.3 Beyond Symmetries Analysis–General Compatibility 147\u003c\/p\u003e \u003cp\u003e4.3.1 Compatibility with First-Order PDEs–Charpit’s Method 149\u003c\/p\u003e \u003cp\u003e4.3.2 Compatibility of Systems 157\u003c\/p\u003e \u003cp\u003e4.3.3 Compatibility of the Nonlinear Heat Equation 159\u003c\/p\u003e \u003cp\u003eExercises 160\u003c\/p\u003e \u003cp\u003e4.4 Concluding Remarks 161\u003c\/p\u003e \u003cp\u003eSolutions 163\u003c\/p\u003e \u003cp\u003eReferences 171\u003c\/p\u003e \u003cp\u003eIndex 175\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406911250775,"sku":"9781118721407","price":73.76,"currency_code":"GBP","in_stock":false}],"url":"https:\/\/bookcurl.com\/products\/symmetry-analysis-of-differential-equations-9781118721407","provider":"Book Curl","version":"1.0","type":"link"}