A First Course in Differential Equations, Modeling, and Simulation

A First Course in Differential Equations, Modeling, and Simulation shows how differential equations arise from applying basic physical principles and experimental observations to engineering systems. Avoiding overly theoretical explanations, the textbook also discusses classical and Laplace transform methods for obtaining the analytical solution of differential equations. In addition, the authors explain how to solve sets of differential equations where analytical solutions cannot easily be obtained. Incorporating valuable suggestions from mathematicians and mathematics professors, the Second Edition: Expands the chapter on classical solutions of ordinary linear differential equations to include additional methods Increases coverage of response of first- and second-order systems to a full, stand-alone chapter to emphasize its importance Includes new examples of applications related to chemical reactions, environmental engineering, biomedical engineering, and biotechnology Contains new exercises that can be used as projects and answers to many of the end-of-chapter problems Features new end-of-chapter problems and updates throughout Thus, A First Course in Differential Equations, Modeling, and Simulation, Second Edition provides students with a practical understanding of how to apply differential equations in modern engineering and science.

IntroductionAn Introductory ExampleDifferential EquationsModelingForcing FunctionsBook ObjectivesSummary Objects in a Gravitational FieldAn ExampleAntidifferentiation: Technique for Solving First-Order Ordinary Differential EquationsBack to Section 2.1Another ExampleSeparation of Variables: Technique for Solving First-Order Ordinary Differential EquationsBack to Section 2.4Equations, Unknowns, and Degrees of FreedomPartial Fraction ExpansionSummary Classical Solutions of Ordinary Linear Differential EquationsExamples of Differential EquationsDefinition of a Linear Differential EquationIntegrating Factor MethodSolution of Homogeneous Differential EquationsSolution of Nonhomogeneous Differential EquationsVariation of ParametersHandling Nonlinearities and Variable CoefficientsTransient and Final ResponsesSummary Laplace TransformsDefinition of the Laplace TransformProperties and Theorems of the Laplace TransformSolution of Differential Equations Using Laplace TransformTransfer FunctionsAlgebraic Manipulations Using Laplace TransformsDeviation VariablesSummary Response of First- and Second-Order SystemsFirst-Order SystemsSecond-Order SystemsExamplesSome Concluding RemarksSummary Mechanical Systems: TranslationalMechanical Law, System Components, and ForcesTypes of SystemsD’Alembert’s Principle and Free Body DiagramsExamplesVertical SystemsSummary Mechanical Systems: RotationalMechanical Law, Moment of Inertia, and TorqueTorsion SpringsRotational DampingGearsSystems with Rotational and Translational ElementsSummary Mass BalancesConservation of MassFlow Rates and ConcentrationsElements and Experimental FactsExamplesExpressions for Mass Transport and Chemical ReactionsAdditional ExamplesApplication to Bioengineering ProcessesFinal CommentsSummaryReferences Thermal SystemsConservation of EnergyModes of Heat TransferConductionConvectionConduction and Convection in SeriesAccumulated or Stored EnergySome ExamplesHeat Transfer in a Flow SystemThermal Effects in a Reactive SystemBoundary Value Problems in Heat TransferSummary Electrical SystemsSome Definitions and ConventionsElectrical Laws, Components, and Initial ConditionsExamples of Electrical CircuitsAdditional ExamplesEnergy and PowerRC Circuits as FiltersSummary Numerical SimulationNumerical Solution of Differential EquationsEuler’s Method for First-Order Ordinary Differential EquationsEuler’s Method for Second-Order Ordinary Differential EquationsStep SizeMore Sophisticated MethodsRepresentation of Differential Equations by Block DiagramsAdditional ExamplesSummaryReference Answers to Selected Problems

Scott W. Campbell has been on the faculty of the Department of Chemical and Biomedical Engineering at the University of South Florida, Tampa, USA, since 1986. He has authored or coauthored more than 60 technical peer-reviewed articles, mostly in the area of thermodynamics, and has received numerous teaching awards at the department, college, university, and state levels. Recently, Professor Campbell has been collaborating with mathematics faculty on application-based teaching of calculus and with College of Education faculty on the training of middle school science and math teachers. Carlos A. Smith is a professor emeritus of chemical engineering at the University of South Florida, Tampa, USA (USF). He has been on the faculty at USF for 43 years, serving in different capacities. Professor Smith has lectured in Europe and many countries in Latin America. He is the coauthor of three editions of a textbook on process control and the author of another book on the same subject. The books have been translated into Spanish and Portuguese.