Author | Holmes, Mark H. author |
---|---|
Title | Introduction to Perturbation Methods [electronic resource] / by Mark H. Holmes |
Imprint | New York, NY : Springer New York, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5347-1 |
Descript | XIII, 356 p. online resource |
1: Introduction to Asymptotic Approximations -- 1.1 Introduction -- 1.2 Taylorโs Theorem and lโHospitalโs Rule -- 1.3 Order Symbols -- 1.4 Asymptotic Approximations -- 1.5 Asymptotic Solution of Algebraic and Transcendental Equations -- 1.6 Introduction to the Asymptotic Solution of Differential Equations -- 1.7 Uniformity -- 1.8 Symbolic Computing -- 2: Matched Asymptotic Expansions -- 2.1 Introduction -- 2.2 Introductory Example -- 2.3 Examples with Multiple Boundary Layers -- 2.4 Interior Layers -- 2.5 Corner Layers -- 2.6 Partial Differential Equations -- 2.7 Difference Equations -- 3: Multiple Scales -- 3.1 Introduction -- 3.2 Introductory Example -- 3.3 Slowly Varying Coefficients -- 3.4 Forced Motion Near Resonance -- 3.5 Boundary Layers -- 3.6 Introduction to Partial Differential Equations -- 3.7 Linear Wave Propagation -- 3.8 Nonlinear Waves -- 3.9 Difference Equations -- 4: The WKB and Related Methods -- 4.1 Introduction -- 4.2 Introductory Example -- 4.3 Turning Points -- 4.4 Wave Propagation and Energy Methods -- 4.5 Wave Propagation and Slender Body Approximations -- 4.6 Ray Methods -- 4.7 Parabolic Approximations -- 4.8 Discrete WKB Method -- 5: The Method of Homogenization -- 5.1 Introduction -- 5.2 Introductory Example -- 5.3 Multidimensional Problem: Periodic Substructure -- 5.4 Porous Flow -- 6: Introduction to Bifurcation and Stability -- 6.1 Introduction -- 6.2 Introductory Example -- 6.3 Analysis of a Bifurcation Point -- 6.4 Linearized Stability -- 6.5 Relaxation Dynamics -- 6.6 An Example Involving a Nonlinear Partial Differential Equation -- 6.7 Bifurcation of Periodic Solutions -- 6.8 Systems of Ordinary Differential Equations -- Appendix AI: Solution and Properties of Transition Layer Equations -- A1.1 Airy Functions -- A1.2 Confluent Hypergeometric Functions -- A1.3 Higher-Order Turning Points -- Appendix A2: Asymptotic Approximations of Integrals -- A2.1 Introduction -- A2.2 Watsonโs Lemma -- A2.3 Laplaceโs Approximation -- A2.4 Stationary Phase Approximation -- Appendix A3: Numerical Solution of Nonlinear Boundary-Value Problems -- A3.1 Introduction -- A3.2 Examples -- A3.3 Computer Code -- References