LEADER 04500nam 22007935 450 001 9910300259103321 005 20251116144813.0 010 $a3-319-23042-5 024 7 $a10.1007/978-3-319-23042-9 035 $a(CKB)3710000000521704 035 $a(SSID)ssj0001585318 035 $a(PQKBManifestationID)16264030 035 $a(PQKBTitleCode)TC0001585318 035 $a(PQKBWorkID)14865450 035 $a(PQKB)10100148 035 $a(DE-He213)978-3-319-23042-9 035 $a(MiAaPQ)EBC6314647 035 $a(MiAaPQ)EBC5592615 035 $a(Au-PeEL)EBL5592615 035 $a(OCoLC)922033492 035 $a(PPN)190532262 035 $a(EXLCZ)993710000000521704 100 $a20150918d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMethods of Mathematical Modelling $eContinuous Systems and Differential Equations /$fby Thomas Witelski, Mark Bowen 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XVIII, 305 p. 50 illus., 45 illus. in color.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-319-23041-7 320 $aIncludes bibliographical references and index. 327 $aRate equations -- Transport equations -- Variational principles -- Dimensional scaling analysis -- Self-similar scaling solutions of differential equations -- Perturbation methods -- Boundary layer theory -- Long-wave asymptotics for PDE problems -- Weakly-nonlinear oscillators -- Fast/slow dynamical systems -- Reduced models for PDE problems -- Modelling in applied fluid dynamics. 330 $aThis book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aDifferential equations 606 $aDifferential equations, Partial 606 $aMathematical physics 606 $aMathematical models 606 $aCalculus of variations 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 615 0$aDifferential equations. 615 0$aDifferential equations, Partial. 615 0$aMathematical physics. 615 0$aMathematical models. 615 0$aCalculus of variations. 615 14$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aCalculus of Variations and Optimal Control; Optimization. 676 $a511.8 700 $aWitelski$b Thomas$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755655 702 $aBowen$b Mark$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300259103321 996 $aMethods of Mathematical Modelling$92536895 997 $aUNINA