Introduction to Perturbation Methods

Przednia okładka
Springer Science & Business Media, 5 gru 2012 - 438

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.

One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.

 

Wybrane strony

Spis treści

Chapter 1 Introduction to Asymptotic Approximations
1
Chapter 2 Matched Asymptotic Expansions
57
Chapter 3 Multiple Scales
139
Chapter 4 The WKB and Related Methods
222
Chapter 5 The Method of Homogenization
297
Chapter 6 Introduction to Bifurcation and Stability
325
Appendix A Taylor Series
393
Appendix B Solution and Properties of Transition Layer Equations
397
Appendix C Asymptotic Approximations of Integrals
407
Apprendix D SecondOrder Difference Equations
411
Appendix E Delay Equations
415
References
420
Index
433
Prawa autorskie

Inne wydania - Wyświetl wszystko

Introduction to Perturbation Methods
Mark H. Holmes
Podgląd niedostępny - 2012
Introduction to Perturbation Methods
Springer
Podgląd niedostępny - 2012
Introduction to Perturbation Methods
Mark H. Holmes
Podgląd niedostępny - 2015
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Kluczowe wyrazy i wyrażenia

amplitude assumed assumption asymptotic approximation asymptotic expansion asymptotically stable bifurcation point boundary conditions boundary layer coefficients composite expansion Consider the problem coordinate curve depends derive determine difference equation differential equation eigenvalues eikonal equation exact solution example Exercise explain Figure Find a first-term Find a two-term first-term approximation first-term expansion following problem function given happens homogenized initial conditions integral interior layer interval limit cycle linear multiple scales nondimensional nonlinear nonzero numerical solution obtain oscillator outer expansion parameter partial differential equations positive constant possible preceding Re(r region regular expansion result satisfies second term Sect secular terms shown in Fig smooth solve Springer Science+Business Media steady Suppose Taylor’s theorem transition layer turning point two-term expansion unstable valid for large variables wave WKB approximation WKB method x-axis zero

Informacje o autorze (2012)

Mark Holmes has written a number of successful textbooks and is Professor at Rensselaar Polytechnic Institute.

Informacje bibliograficzne

TytułIntroduction to Perturbation Methods
Tom 20 z Texts in Applied Mathematics
AutorMark H. Holmes
Wydanie2, ilustrowane
WydawcaSpringer Science & Business Media, 2012
ISBN1461454778, 9781461454779
Liczba stron438
  
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