
Elements of Advanced Enginnering Mathematics
O’Neil, Peter

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This book is intended to provide students with an efficient introduction and accessibility to ordinary and partial differential equations, linear algebra, vector analysis, Fourier analysis, and special functions and eigenfunction expansions, for their use as tools of inquiry and analysis in modeling and problem solving. It should also serve as preparation for further reading where this suits individual needs and interests.
Although much of this material appears in Advanced Engineering Mathematics, 6th edition, Elements has been completely rewritten to provide a natural flow of the material in this shorter format.
Many types of computations, such as construction of direction fields, or the manipulation Bessel functions and Legendre polynomials in writing eigenfunction expansions, require the use of software packages. A short MAPLE primer is included as Appendix B. This is designed to enable the student to quickly master the use of MAPLE for such computations. Other software packages can also be used.
Features
This new text incorporates Maple™ by Maplesoft®  a world leader in mathematical and analytical software Rigorous engineering mathematics topics are now made accessible with the emphasis of visuals, numerous examples, and interesting mathematical models Provides students with an efficient introduction to the required math necessary for engineering as well as the tools for inquiry and analysis used in modeling and problem solving. A separate Student’s Solutions Manual is available
PART 1: ORDINARY DIFFERENTIAL EQUATIONS 1. FirstOrder Differential Equations 2. Linear SecondOrder Equations 3. The Laplace Transform 4. Series Solutions PART 2: VECTORS, LINEAR ALGEBRA, AND SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS 5. Algebra and Geometry of Vectors 6. Matrices and Systems of Linear Equations 7. Determinants 8. Eigenvalues and Diagonalization 9. Systems of Linear Differential Equations PART 3: VECTOR ANALYSIS 10. Vector Differential Calculus 11. Vector Integral Calculus PART 4: FOURIER ANALYSIS AND EIGENFUNCTION EXPANSIONS 12. Fourier Series 13. The Fourier Integral and Transforms 14. Eigenfunction Expansions PART 5: PARTIAL DIFFERENTIAL EQUATIONS 15. The Wave Equation 16. The Heat Equation 17. The Potential Equation APPENDIX A. GUIDE TO NOTATION APPENDIX B. A MAPLE PRIMER
{NewFeatures} {Supplements} {Quotes} Peter V. O’Neil Served on the faculty at the University of Minnesota, The College of William and Mary in Virginia, where he was chairman of mathematics, and the University of Alabama at Birmingham, where he was chairman of mathematics, dean of natural sciences and mathematics, and university provost. Primary research interests are in graph theory, combinatorial analysis and applications of mathematics to problems in the physical and biological sciences and engineering.
HomeInstructors New TitlesGeneral Chemistry TextbookPhysics for the Life Sciences TextbookOrder Inspection CopiesOnline ResourcesTechnology SupportRep locatorStudents Online Student ResourcesBookshopsAuthors Review processProposal guidelinesCengage Learning eTextbook Collection biz/ed premierCengage Learning eTextbook CollectionCustom Publishing Create Your Own Custom SolutionSignature Labs and FlextextFAQsHow to get startedUnited KingdomChange your regionSearch Go AccountingBusiness & TechnologyBusiness CommunicationBusiness EducationBusiness LawBusiness MathematicsBusiness StatisticsCareer Investigation & ReadinessCertificationCommunicationsComputer ApplicationsComputer EducationDecision SciencesEconomicsFinanceIntroduction to BusinessManagementMarketingOffice TechnologyReal EstateReferenceTaxationTechnologyAnthropologyArtCommunication and MediaCounselling/PsychotherapyCriminal JusticeDevelopmental EnglishEnglishEnglish as a Second LanguageFrenchGermanHistoryHuman ServicesItalianModern LanguageMusicPhilosophyPolitical SciencePsychologyReligionSocial WorkSociologySpanishAstronomyChemistryEarth ScienceEngineeringHealthLife SciencesMathematicsNutritionOceanographyPhysicsAssessment, Training, and ProjectsComputer ConceptsComputer ScienceDatabasesGame Design & DevelopmentGraphic CommunicationsHelp Desk/Desktop SupportInternetMedia Arts & DesignMISMusic TechnologyNetworking & SecurityOffice SuitesOperating SystemsPC Repair/A+Presentation ToolsProgrammingProject ManagementSoft SkillsSpreadsheetsWeb Design & DevelopmentWord ProcessingAgriscienceAutomotive and MechanicsAviationCatering and HospitalityCollege SuccessEducationElectronics and EngineeringHair & BeautyLeisure and ToursimNursing, Medical and DentistryPhotography, Multimedia and DesignProfessional Development and Study SkillsTradesAbout Cengage LearningEnglish Language TeachingGlobalHigher EducationLibrary & ReferenceCengage Learning Investor InformationAbout UsCopyright, Terms & ConditionsPrivacy PolicyContact UsCareersWebsite Design by Mulberry Interactive Ltd 
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PART 1: ORDINARY DIFFERENTIAL EQUATIONS 1. FirstOrder Differential Equations 2. Linear SecondOrder Equations 3. The Laplace Transform 4. Series Solutions PART 2: VECTORS, LINEAR ALGEBRA, AND SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS 5. Algebra and Geometry of Vectors 6. Matrices and Systems of Linear Equations 7. Determinants 8. Eigenvalues and Diagonalization 9. Systems of Linear Differential Equations PART 3: VECTOR ANALYSIS 10. Vector Differential Calculus 11. Vector Integral Calculus PART 4: FOURIER ANALYSIS AND EIGENFUNCTION EXPANSIONS 12. Fourier Series 13. The Fourier Integral and Transforms 14. Eigenfunction Expansions PART 5: PARTIAL DIFFERENTIAL EQUATIONS 15. The Wave Equation 16. The Heat Equation 17. The Potential Equation APPENDIX A. GUIDE TO NOTATION APPENDIX B. A MAPLE PRIMER
{NewFeatures} {Supplements} {Quotes} Peter V. O’Neil Served on the faculty at the University of Minnesota, The College of William and Mary in Virginia, where he was chairman of mathematics, and the University of Alabama at Birmingham, where he was chairman of mathematics, dean of natural sciences and mathematics, and university provost. Primary research interests are in graph theory, combinatorial analysis and applications of mathematics to problems in the physical and biological sciences and engineering.
HomeInstructors New TitlesGeneral Chemistry TextbookPhysics for the Life Sciences TextbookOrder Inspection CopiesOnline ResourcesTechnology SupportRep locatorStudents Online Student ResourcesBookshopsAuthors Review processProposal guidelinesCengage Learning eTextbook Collection biz/ed premierCengage Learning eTextbook CollectionCustom Publishing Create Your Own Custom SolutionSignature Labs and FlextextFAQsHow to get startedUnited KingdomChange your regionSearch Go AccountingBusiness & TechnologyBusiness CommunicationBusiness EducationBusiness LawBusiness MathematicsBusiness StatisticsCareer Investigation & ReadinessCertificationCommunicationsComputer ApplicationsComputer EducationDecision SciencesEconomicsFinanceIntroduction to BusinessManagementMarketingOffice TechnologyReal EstateReferenceTaxationTechnologyAnthropologyArtCommunication and MediaCounselling/PsychotherapyCriminal JusticeDevelopmental EnglishEnglishEnglish as a Second LanguageFrenchGermanHistoryHuman ServicesItalianModern LanguageMusicPhilosophyPolitical SciencePsychologyReligionSocial WorkSociologySpanishAstronomyChemistryEarth ScienceEngineeringHealthLife SciencesMathematicsNutritionOceanographyPhysicsAssessment, Training, and ProjectsComputer ConceptsComputer ScienceDatabasesGame Design & DevelopmentGraphic CommunicationsHelp Desk/Desktop SupportInternetMedia Arts & DesignMISMusic TechnologyNetworking & SecurityOffice SuitesOperating SystemsPC Repair/A+Presentation ToolsProgrammingProject ManagementSoft SkillsSpreadsheetsWeb Design & DevelopmentWord ProcessingAgriscienceAutomotive and MechanicsAviationCatering and HospitalityCollege SuccessEducationElectronics and EngineeringHair & BeautyLeisure and ToursimNursing, Medical and DentistryPhotography, Multimedia and DesignProfessional Development and Study SkillsTradesAbout Cengage LearningEnglish Language TeachingGlobalHigher EducationLibrary & ReferenceCengage Learning Investor InformationAbout UsCopyright, Terms & ConditionsPrivacy PolicyContact UsCareersWebsite Design by Mulberry Interactive Ltd 

