Mathematical methods in chemical and biological engineering

Content: Architecture of Mathematical ModelsIntroductionClassification of Mathematical Models in Chemical and Biological EngineeringModels Resulting in Algebraic Equations: Lumped-Parameter, Steady-State ModelsModels Resulting in Ordinary Differential Equations: Initial Value ProblemsModels Resulting in Ordinary Differential Equations: Boundary Value ProblemsModels Resulting in Partial Differential EquationsModel Equations in Non-Dimensional FormConcluding CommentsExercise ProblemsReferencesOrdinary Differential Equations and ApplicationsIntroductionReview of Solution of Ordinary Differential EquationsThe Laplace Transform TechniqueMatrix Method of Solution of Simultaneous ODEsConcluding CommentsExercise ProblemsReferencesSpecial Functions and Solutions of Ordinary Differential Equations with Variable CoefficientsIntroductionThe Gamma FunctionThe Beta FunctionThe Error FunctionThe Gamma DistributionSeries Solution of Linear Second-Order ODEs with Variable CoefficientsSeries Solution of Linear Second-Order ODEs Leading to Special FunctionsLegendre Differential Equation and the Legendre FunctionsHypergeometric FunctionsConcluding CommentsExercise ProblemsReferencesPartial Differential EquationsIntroductionCommon Second Order PDEs in Science and EngineeringBoundary Value ProblemsTypes of Boundary ConditionsTechniques of Analytical Solution of a Second Order PDEExamples: Use of the Technique of Separation of VariablesSolution of Non-Homogeneous PDEsSimilarity SolutionMoving Boundary ProblemsPrinciple of SuperpositionGreen\'s FunctionConcluding CommentsExercise ProblemsReferencesIntegral TransformsIntroductionDefinition of an Integral TransformFourier TransformLaplace TransformApplication to Engineering ProblemsConcluding CommentsExercise ProblemsReferencesApproximate Methods of Solution of Model EquationsIntroductionOrder SymbolsAsymptotic ExpansionPerturbation MethodsConcluding CommentsExercise ProblemsReferencesAnswers to Selected Exercise ProblemsAppendix A: Topics in MatricesAppendix B: Fourier Series Expansion and Fourier Integral TheoremAppendix C: Review of Complex VariablesAppendix D: Selected Formulas and Identities
 Dirac Delta Function and Heaviside FunctionAppendix E: Brief Table of Inverse Laplace TransformsAppendix F: Some Detailed DerivationsView a List of Solved Examples.