Differential Equations with Mathematica

PrefaceChapter 1: Introduction to Differential Equations 1.1 Purpose 1.2 Definitions and Concepts 1.3 Solutions of Differential Equations 1.4 Initial and Boundary Value ProblemsChapter 2: First-Order Ordinary Differential Equations 2.1 Separation of Variables 2.2 Homogeneous Equations 2.3 Exact Equations 2.4 Linear Equations 2.5 Some Special First-Order Equations 2.6 Theory of First-Order EquationsChapter 3: Applications of First-Order Ordinary Differential Equations 3.1 Orthogonal Trajectories 3.2 Direction Fields 3.3 Population Growth and Decay 3.4 Newton's Law of Cooling 3.5 Free-Falling BodiesChapter 4: Higher Order Differential Equations 4.1 Preliminary Definitions and Notation 4.2 Solutions of Homogeneous Equations with Constant Coefficients 4.3 Nonhomogeneous Equations with Constant Coefficients: The Annihilator Method 4.4 Nonhomogeneous Equations with Constant Coefficients: Variation of Parameters 4.5 Ordinary Differential Equations with Nonconstant Coefficients: Cauchy-Euler Equations 4.6 Ordinary Differential Equations with Nonconstant Coefficients: Exact Second-Order, Autonomous, and Equidimensional EquationsChapter 5: Applications of Higher Order Differential Equations 5.1 Simple Harmonic Motion 5.2 Damped Motion 5.3 Forced Motion 5.4 L-R-C Circuits 5.5 Deflection of a Beam 5.6 The Simple PendulumChapter 6: Power Series Solutions of Ordinary Differential Equations 6.1 Power Series Review 6.2 Power Series Solutions about Ordinary Points 6.3 Power Series Solutions about Regular Singular PointsChapter 7: Applications of Power Series 7.1 Applications of Power Series Solutions to Cauchy-Euler Equations 7.2 The Hypergeometric Equation 7.3 The Vibrating CableChapter 8: Introduction to the Laplace Transform 8.1 The Laplace Transform: Preliminary Definitions and Notation 8.2 Solving Ordinary Differential Equations with the Laplace Transform 8.3 Some Special Equations: Delay Equations, Equations with Nonconstant CoefficientsChapter 9: Applications of the Laplace Transform 9.1 Spring-Mass Systems Revisited 9.2 L-R-C Circuits Revisited 9.3 Population Problems Revisited 9.4 The Convolution Theorem 9.5 Differential Equations Involving Impulse FunctionsChapter 10: Systems of Ordinary Differential Equations 10.1 Review of Matrix Algebra and Calculus 10.2 Preliminary Definitions and Notation 10.3 Homogeneous Linear Systems with Constant Coefficients 10.4 Variation of Parameters 10.5 Laplace Transforms 10.6 Nonlinear Systems, Linearization, and Classification of Equilibrium PointsChapter 11: Applications of Systems of Ordinary Differential Equations 11.1 L-R-C Circuits with Loops 11.2 Diffusion Problems 11.3 Spring-Mass Systems 11.4 Population Problems 11.5 Applications Using Laplace TransformsChapter 12: Fourier Series and Applications to Partial Differential Equations 12.1 Orthogonal Functions and Sturm-Liouville Problems 12.2 Introduction to Fourier Series 12.3 The One-Dimensional Heat Equation 12.4 The One-Dimensional Wave Equation 12.5 Laplace's Equation 12.6 The Two-Dimensional Wave Equation in a Circular RegionAppendix: Numerical Methods Euler's Method The Runge-Kutta Method Systems of Differential Equations Error AnalysisGlossary of Mathematica CommandsSelected ReferencesIndex