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Architecture of Mathematical Models Introduction Classification of Mathematical Models in Chemical and Biological Engineering Models Resulting in Algebraic Equations: Lumped-Parameter, Steady-State Models Models Resulting in Ordinary Differential Equations: Initial Value Problems Models Resulting in Ordinary Differential Equations: Boundary Value Problems Models Resulting in Partial Differential Equations Model Equations in Non-Dimensional Form Concluding Comments Exercise Problems References Ordinary Differential Equations and Applications Introduction Review of Solution of Ordinary Differential Equations The Laplace Transform Technique Matrix Method of Solution of Simultaneous ODEs Concluding Comments Exercise Problems References Special Functions and Solutions of Ordinary Differential Equations with Variable Coefficients Introduction The Gamma Function The Beta Function The Error Function The Gamma Distribution Series Solution of Linear Second-Order ODEs with Variable Coefficients Series Solution of Linear Second-Order ODEs Leading to Special Functions Legendre Differential Equation and the Legendre Functions Hypergeometric Functions Concluding Comments Exercise Problems References Partial Differential Equations Introduction Common Second Order PDEs in Science and Engineering Boundary Value Problems Types of Boundary Conditions Techniques of Analytical Solution of a Second Order PDE Examples: Use of the Technique of Separation of Variables Solution of Non-Homogeneous PDEs Similarity Solution Moving Boundary Problems Principle of Superposition Green's Function Concluding Comments Exercise Problems References Integral Transforms Introduction Definition of an Integral Transform Fourier Transform Laplace Transform Application to Engineering Problems Concluding Comments Exercise Problems References Approximate Methods of Solution of Model Equations Introduction Order Symbols Asymptotic Expansion Perturbation Methods Concluding Comments Exercise Problems References Answers to Selected Exercise Problems Appendix A: Topics in Matrices Appendix B: Fourier Series Expansion and Fourier Integral Theorem Appendix C: Review of Complex Variables Appendix D: Selected Formulas and Identities; Dirac Delta Function and Heaviside Function Appendix E: Brief Table of Inverse Laplace Transforms Appendix F: Some Detailed Derivations View a List of Solved Examples
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