LEADER 04735nam 22006495 450 001 9910254277003321 005 20200701115535.0 010 $a3-319-59993-3 024 7 $a10.1007/978-3-319-59993-9 035 $a(CKB)4340000000062060 035 $a(DE-He213)978-3-319-59993-9 035 $a(MiAaPQ)EBC5591750 035 $a(PPN)203669312 035 $a(EXLCZ)994340000000062060 100 $a20170726d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFractional and Multivariable Calculus $eModel Building and Optimization Problems /$fby A.M. Mathai, H.J. Haubold 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XIII, 234 p. 7 illus.) 225 1 $aSpringer Optimization and Its Applications,$x1931-6828 ;$v122 311 $a3-319-59992-5 327 $a1. Essential of Fractional Calculus -- 2. Multivariable Calculus -- 3. Deterministic Models and Optimization -- 4. Non-deterministic Models and Optimization -- 5. Optimal Regression Designs. ?Index. 330 $aThis textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable functions). Illustrative examples, input-output process, optimal recovery of functions and approximations are given; each section lists an ample number of exercises to heighten understanding of the material. Chapter three discusses deterministic/mathematical and optimization models evolving from differential equations, difference equations, algebraic models, power function models, input-output models and pathway models. Fractional integral and derivative models are examined. Chapter four covers non-deterministic/stochastic models. The random walk model, branching process model, birth and death process model, time series models, and regression type models are examined. The fifth chapter covers optimal design. General linear models from a statistical point of view are introduced; the Gauss?Markov theorem, quadratic forms, and generalized inverses of matrices are covered. Pathway, symmetric, and asymmetric models are covered in chapter six, the concepts are illustrated with graphs. . 410 0$aSpringer Optimization and Its Applications,$x1931-6828 ;$v122 606 $aMathematical models 606 $aMathematical optimization 606 $aFunctions, Special 606 $aIntegral transforms 606 $aCalculus, Operational 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 606 $aOptimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26008 606 $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X 606 $aIntegral Transforms, Operational Calculus$3https://scigraph.springernature.com/ontologies/product-market-codes/M12112 615 0$aMathematical models. 615 0$aMathematical optimization. 615 0$aFunctions, Special. 615 0$aIntegral transforms. 615 0$aCalculus, Operational. 615 14$aMathematical Modeling and Industrial Mathematics. 615 24$aOptimization. 615 24$aSpecial Functions. 615 24$aIntegral Transforms, Operational Calculus. 676 $a515.83 700 $aMathai$b A.M$4aut$4http://id.loc.gov/vocabulary/relators/aut$055903 702 $aHaubold$b H.J$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254277003321 996 $aFractional and Multivariable Calculus$92053544 997 $aUNINA