Singular Perturbation Theory [electronic resource] : Mathematical and Analytical Techniques with Applications to Engineering / by R. S. Johnson.Material type: TextLanguage: English Publisher: Boston, MA : Springer US, 2005Description: XVI, 292 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387232171Subject(s): Engineering | Differential Equations | Mathematics | Mathematical physics | Engineering mathematics | Hydraulic engineering | Engineering | Appl.Mathematics/Computational Methods of Engineering | Applications of Mathematics | Mathematical and Computational Physics | Engineering Fluid Dynamics | Ordinary Differential EquationsAdditional physical formats: Printed edition:: No titleDDC classification: 519 LOC classification: TA329-348TA640-643Online resources: Click here to access online
Mathematical Preliminaries -- Introductory Applications -- Further Applications -- The Method of Multiple Scales -- Some Worked Examples Arising from Physical Problems.
Many areas of science and engineering produce difficult mathematical problems , i.e., problems that cannot be solved in any conventional sense. In many cases, against all the apparent odds, it is possible to construct systematic approximations that lead to useful solutions. The most powerful of these approximation techniques is singular perturbation theory. Singular Perturbation Theory introduces all the background ideas to this subject, designed for those with only the most superficial familiarity with university-level mathematics. The methods are developed through worked examples and set exercises (with answers); the latter part of the book is devoted to applications drawn from: mechanics, physics, semi- and superconductor theory, fluid mechanics, thermal processes, chemical and biochemical reactions. In a novel approach, these are grouped together so that the reader with particular interests can readily access them. This book is based on material that has been taught, mainly by the author, to MSc and research students in applied mathematics and engineering mathematics at the University of Newcastle upon Tyne over the last thirty years. The aim of this text is to make all the material readily accessible to the reader who wishes to learn and use the ideas to help with research problems and who does not have a strong mathematical background.