Download e-book for kindle: A First Look at Perturbation Theory 2nd Edition by James G., Mann Jr., James E., Physics Simmonds

By James G., Mann Jr., James E., Physics Simmonds

ISBN-10: 0486675513

ISBN-13: 9780486675510

Emphasizing the "why" in addition to the "how," this beneficial and well-written introductory textual content explains tools for acquiring approximate recommendations to mathematical difficulties by means of exploiting the presence of small, dimensionless parameters. aimed at undergraduates in engineering and the actual sciences. Preface. Bibliography. Appendixes.

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Example text

A shell by a membrane) , we shall say that such a BVP exhibits a singu larity in the m odel. We can n ow answer, to some extent, the two questions we posed earlier. 6) outside a boundary layer at t = o . For this reason, Ae-t is called the interior contribution t o y et , f) . Second , because there is n o boundary layer near t = 1 , A can be determined from the BC at t = 1 . In the chapters to follow, we shall develop systematic methods for re­ ducing singular perturbation problems to regular ones.

6) often corresponds to replacing a physical model by a simpler one ( e . g . , a shell by a membrane) , we shall say that such a BVP exhibits a singu larity in the m odel. We can n ow answer, to some extent, the two questions we posed earlier. 6) outside a boundary layer at t = o . For this reason, Ae-t is called the interior contribution t o y et , f) . Second , because there is n o boundary layer near t = 1 , A can be determined from the BC at t = 1 . In the chapters to follow, we shall develop systematic methods for re­ ducing singular perturbation problems to regular ones.

Most importantly, the solution of the DE will be a function of both f and the independent variable, say t, which immediately raises the question of whether certain approximate solution are uniformly accu­ rate for all values of t in the domain of interest . Fortunately, when f is small , characterizing the f-dependence of the solution of a DE with Ie 's or Be's simplifies. The rest of this book is 39 44 Singular Perturbations in Ordin ary Differential Equations The term e-t / f is called a boundary layer ( or the b oundary layer con­ tribution to yet , f» because it is significant only in a narrow layer of width O ( f) near the b oun d ary t = o.

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A First Look at Perturbation Theory 2nd Edition by James G., Mann Jr., James E., Physics Simmonds


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