LEADER 04704nam 22007695 450 001 9910821729303321 005 20240516013805.0 010 $a1-4757-3069-1 024 7 $a10.1007/978-1-4757-3069-2 035 $a(CKB)2660000000022255 035 $a(SSID)ssj0001295709 035 $a(PQKBManifestationID)11777907 035 $a(PQKBTitleCode)TC0001295709 035 $a(PQKBWorkID)11342818 035 $a(PQKB)11774547 035 $a(DE-He213)978-1-4757-3069-2 035 $a(MiAaPQ)EBC3087185 035 $a(PPN)238050688 035 $a(EXLCZ)992660000000022255 100 $a20130125d1999 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aAdvanced Mathematical Methods for Scientists and Engineers I $eAsymptotic Methods and Perturbation Theory /$fby Carl M. Bender, Steven A. Orszag 205 $a1st ed. 1999. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1999. 215 $a1 online resource (XIV, 593 p.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-98931-5 311 $a1-4419-3187-2 320 $aIncludes bibliographical references and index. 327 $aI Fundamentals -- 1 Ordinary Differential Equations -- 2 Difference Equations -- II Local Analysis -- 3 Approximate Solution of Linear Differential Equations -- 4 Approximate Solution of Nonlinear Differential Equations -- 5 Approximate Solution of Difference Equations -- 6 Asymptotic Expansion of Integrals -- III Perturbation Methods -- 7 Perturbation Series -- 8 Summation of Series -- IV Global Analysis -- 9 Boundary Layer Theory -- 10 WKB Theory -- 11 Multiple-Scale Analysis. 330 $aThe triumphant vindication of bold theories-are these not the pride and justification of our life's work? -Sherlock Holmes, The Valley of Fear Sir Arthur Conan Doyle The main purpose of our book is to present and explain mathematical methods for obtaining approximate analytical solutions to differential and difference equations that cannot be solved exactly. Our objective is to help young and also establiShed scientists and engineers to build the skills necessary to analyze equations that they encounter in their work. Our presentation is aimed at developing the insights and techniques that are most useful for attacking new problems. We do not emphasize special methods and tricks which work only for the classical transcendental functions; we do not dwell on equations whose exact solutions are known. The mathematical methods discussed in this book are known collectively as­ asymptotic and perturbative analysis. These are the most useful and powerful methods for finding approximate solutions to equations, but they are difficult to justify rigorously. Thus, we concentrate on the most fruitful aspect of applied analysis; namely, obtaining the answer. We stress care but not rigor. To explain our approach, we compare our goals with those of a freshman calculus course. A beginning calculus course is considered successful if the students have learned how to solve problems using calculus. 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aPhysics 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aPhysics. 615 14$aAnalysis. 615 24$aMathematical and Computational Engineering. 615 24$aMathematical Methods in Physics. 615 24$aNumerical and Computational Physics, Simulation. 676 $a515 676 $a515.35 686 $a34E05$2msc 686 $a34A45$2msc 686 $a41A60$2msc 700 $aBender$b Carl M$4aut$4http://id.loc.gov/vocabulary/relators/aut$021730 702 $aOrszag$b Steven A$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910821729303321 996 $aAdvanced Mathematical Methods for Scientists and Engineers I$94076035 997 $aUNINA