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DIFFERENTIAL EQUATION ANALYSIS IN BIOMEDICAL SCIENCE AND ENGINEERING DIFFERENTIAL EQUATION ANALYSIS IN BIOMEDICAL SCIENCE AND ENGINEERING ORDINARY DIFFERENTIAL EQUATION APPLICATIONS WITH R William E. Schiesser Department of Chemical Engineering Lehigh University Bethlehem, PA CoverDesign:Wiley CoverIllustration:Courtesyoftheauthor Copyright©2014byJohnWiley&Sons,Inc.Allrightsreserved. PublishedbyJohnWiley&Sons,Inc.,Hoboken, NewJersey. PublishedsimultaneouslyinCanada. Nopartofthispublication maybereproduced,storedinaretrievalsystem,ortransmitted inanyformorbyanymeans,electronic, mechanical, photocopying,recording,scanning, orotherwise,exceptaspermittedunderSection107or108ofthe1976UnitedStates CopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,or authorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearance Center,Inc.,222RosewoodDrive,Danvers,MA01923,(978)750-8400,fax(978) 750-4470,oronthewebatwww.copyright.com. RequeststothePublisherforpermission shouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,111River Street,Hoboken,NJ07030,(201)748-6011,fax(201)748-6008,oronlineat http://www.wiley.com/go/permission. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheir besteffortsinpreparingthisbook,theymakenorepresentationsorwarrantieswithrespect totheaccuracy orcompletenessofthecontentsofthisbookandspecificallydisclaimany impliedwarrantiesofmerchantability orfitnessforaparticularpurpose.Nowarrantymay becreatedorextendedbysalesrepresentativesorwrittensalesmaterials.Theadviceand strategiescontained hereinmaynotbesuitableforyoursituation.Youshouldconsultwith aprofessionalwhereappropriate.Neitherthepublishernorauthorshallbeliableforany lossofprofitoranyothercommercial damages,includingbutnotlimitedtospecial, incidental, consequential,orotherdamages. Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,please contactourCustomerCareDepartmentwithintheUnitedStatesat(800)762-2974,outside theUnitedStatesat(317)572-3993orfax(317)572-4002. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthat appears inprintmaynotbeavailable inelectronicformats.Formoreinformationabout Wileyproducts,visitourwebsiteatwww.wiley.com. LibraryofCongressCataloging-in-PublicationData: Schiesser,W.E. Differentialequationanalysisinbiomedical scienceandengineering : ordinary differentialequationapplications withR/WilliamE.Schiesser,DepartmentofChemical Engineering,LehighUniversity,Bethlehem,PA. pagescm Includes bibliographicalreferences andindex. ISBN978-1-118-70548-3(cloth) 1. Biomedicalengineering–Mathematics. 2. Biomathematics. 3. Bioreactors–Data processing. 4. Differentialequations. I.Title. R857.M34O342013 610.280285–dc23 2013020440 PrintedintheUnitedStatesofAmerica. 10987654321 To John Backus and Leon Lapidus, and their research groups CONTENTS Preface ix 1. Introduction to Ordinary Differential Equation Analysis: Bioreactor Dynamics 1 2. Diabetes Glucose Tolerance Test 79 3. Apoptosis 145 4. Dynamic Neuron Model 191 5. Stem Cell Differentiation 217 6. Acetylcholine Neurocycle 241 7. Tuberculosis with Differential Infectivity 321 8. Corneal Curvature 337 AppendixA1:Stiff ODE Integration 375 Index 417 vii

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