1 Introduction and General Outline. - References. - 2 Concepts of Continuous Transformation Groups. - 2. 0 Introduction. - 2. 1 Group Approach. - 2. 2 Transformation Groups. - 2. 3 The Concept of an Infinitesimal Transformation. - 2. 4 Relation Between Global and Infinitesimal Groups Transformations. - 2. 5 The Concept of Invariance. - 2. 6 Invariance of Differential Equations Under Groups of Transformations. - 2. 7 The Extended Group of Transformations. - 2. 8 The Characteristic Function. - 2. 9 Transformations Involving Two Independent Variables. - 2. 10 Transformation Involving Two Dependent and Two Independent Variables. - 2. 11 Dimensional and Affine Groups of Transformations. - 2. 12 Summary. - References. - 3 A Survey of Methods for Determining Similarity. - 3. 0 Introduction. - 3. 1 Direct Methods. - 3. 2 Group-Theoretic Methods. - 3. 3 Summary. - References. - 4 Application of Similarity Analysis to Problems in Sciences and Engineering. - 4. 0 Introduction. - 4. 1 Laminar Two Dimensional Jet:Separation of Variable Method. - 4. 2 Impact of Rods With Nonlinear Material Properties: Separation of Variables Method. - 4. 3 Diffusion of Vorticity From a Line Vortex Immersed in a Quiescent Fluid: Dimensional Method. - 4. 4 Laminar Boundary Layer Equation: Dimensional Method. - 4. 5 Free Convection From a Vertical Needle: Heliums Churchill Method. - 4. 6 Deflection of a Semi-Infinite Wedge Shaped Plate: Birkhoff-Morgan Method. - 4. 7 Heated Jet: Birkhoff-Morgan Method. - 4. 8 Unsteady One-Dimensional Gas Dynamics Equations: Characteristic Function Method. - 4. 9 Summary. - References. - 5 Similarity Analysis of Boundary Value Problems With Finite Boundaries. - 5. 0 Introduction. - 5. 1 Boundary Value Problems With Moving Boundaries. - 5. 2 Invariant Boundary and Surface Description. - 5. 3 Invariance Under Groups Other Than Dimensional Groups. - 5. 4 Summary. - References. - 6 On Obtaining Non-Similar Solutions From Similar Solutions. - 6. 0 Introduction. - 6. 1 Superposition of Similarity Solutions. - 6. 2 The Use of Fundamental Solutions. - 6. 3 Pseudo-Similarity Transformations. - 6. 4 Similarity Solutions as Asymptotic Limits of the Non-Similar Problem Description. - 6. 5 Summary. - References. - 7 Moving Boundary Problems Governed by Parabolic Equations. - 7. 0 Introduction. - 7. 1 Problems With Phase Change. - 7. 2 Problems Without Phase Change. - 7. 3 Summary. - References. - 8 Similarity Analysis of Wave Propagation Problems. - 8. 0 General. - 8. 1 Propagation Along Characteristics. - 8. 2 Non-Characteristic Propagation:Shock Waves. - 8. 3 Non-Characteristic Propagation:Uniform Propagation Regime. - 8. 4 From Translation to Dimensional Group Invariance. - 8. 5 Summary. - References. - 9 Transformation of a Boundary Value Problem to an Initial Value Problem. - 9. 0 Introduction. - 9. 1 Blasius Equation in Boundary Layer Flow. - 9. 2 Longitudinal Impact of Nonlinear Viscoplastic Rods. - 9. 3 Summary. - References. - 10 From Nonlinear to Linear Differential Equations Using Transformation Groups. - 10. 1 From Nonlinear to Linear Differential Equations. - 10. 2 Application to Ordinary Differential Equations Bernoulli's Equation. - 10. 3 Application to Partial Differential Equations A Nonlinear Chemical Exchange Process. - 10. 4 Limitations of the Inspectional Group Method. - 10. 5 Summary. - References. - 11 Miscellaneous Topics. - 11. 1 Reduction of Differential Equations to Algebraic Equations. - 11. 2 Reduction of Order of an Ordinary Differential Equation. - 11. 3 Transformation From Ordinary to Partial Differential Equations-Search for First Integrals. - 11. 4 Reduction of Number of Variables by Multiparameter Groups of Transformations. - 11. 5 Self-SimilarSolutions of the First and Second Kind. - 11. 6 Normalized Representation and Dimensional Consideration. - References. - Problems. Language: English