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

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

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C) ii + y = f cos t , O < t y eO) = 0, yeO) = 1 .

4. Explain how one or more of the points dis cussed at the beginning of the Chapter is illustrated by each of the following problems. Also explain why each is a s i ngul ar perturbation problem. (Note th at all may be solved exactly. ) (a) ii + ( 1 + f)Y = 0, 0 < t < 7r y e O ) = 0 , y ( 7r ) = fP , p > O. (b) t 2 ii + ty = 0 , f < t < 1 y(f) = 1 , y(l) = o. (c) ii + y = f cos t , O < t y eO) = 0, yeO) = 1 .

4. 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.