1 Introduction to Differential Equations 1.1 Differential Equation Models 1.2 The Derivative 1.3 Integration 2 First-Order Equations 2.1 Differential Equations and Solutions 2.2 Solutions to Separable Equations 2.3 Models of Motion 2.4 Linear Equations 2.5 Mixing Problems 2.6 Exact Differential Equations 2.7 Existence and Uniqueness of Solutions 2.8 Dependence of Solutions on Initial Conditions 2.9 Autonomous Equations and Stability Project 2.10 The Daredevil Skydiver 3 Modeling and Applications 3.1 Modeling Population Growth 3.2 Models and the Real World 3.3 Personal Finance 3.4 Electrical Circuits Project 3.5 The spruce Budworm Project 3.6 Social Security, Now or Later 4 Second-Order Equations 4.1 Definitions and Examples 4.2 Second-Order Equations and Systems 4.3 Linear, Homogeneous Equations with Constant Coefficients 4.4 Harmonic Motion 4.5 Inhomogeneous Equations ; the Method of Undetermined Coefficiensts 4.6 Variation of Parameters 4.7 Forced Harmonic Motion Project 4.8 Nonlinear Oscillators 5 The Laplace Transform 5.1 The Definition of the Laplace Transform 5.2 Basic Properties of the Laplace Transform 5.3 The Inverse Laplace Transform 5.4 Using the Laplace Transform to Solve Differential Equations 5.5 Discontinuous Forcing Terms 5.6 The Delta Function 5.7 Convolutions 5.8 Summary Project 5.9 Forced Harmonic Oscillators 6 Numerical Methods 6.1 Euler's Method 6.2 Runge-Kutta Methods 6.3 Numerical Error Comparisons 6.4 Practical Use of Solvers Project 6.5 Numerical Error Comparison 7 Matrix Algebra 7.1 Vectors and Matrices 7.2 Systems of Linear Equations with Two or Three Variables 7.3 Solving Systems of Equations 7.4 Homogeneous and Inhomogeneous Systems 7.5 Bases of a Subspace 7.6 Square Matrices 7.7 Determinants 8 An Introduction to Systems 8.1 Definitions and Examples 8.2 Geometric Interpretation of Solutions 8.3 Qualitative Analysis 8.4 Linear Systems 8.5 Properties of Linear Systems Project 8.6 Long-Term Behavior of Solutions 9 Linear Systems with Constant Coefficienst 9.1Overview of the Technique 9.2 Planar Systems 9.3 Phase Plane Portraits 9.4 The Trace-Determinant Plane 9.5 Higher-Dimensional Systems 9.6 The Exponential of Matrix 9.7 Qualitative Analysis of Linear Systems 9.8 Higer-Order Linear Equations 9.9 Inhomogeneous Linear Systems Project 9.10 Phase Plane Portraits Project 9.11 Oscillations of Linear Molecules 10 Nonlinear Systems 10.1 The Linearization of a Nonlinear System 10.2 Long-Term Behavior of Solutions 10.3 Invariant Sets and the Use of Nullclines 10.4 Long-Term Behavior of Solutions to Planar Systems 10.5 Conserved Quantities 10.6 Nonlinear Mechanics 10.7 The Method of Lyapunov 10.8 Predator-Prey Systems Project 10.9 Human lmmune Response to Infectious Disease Project 10.10 Analysis of Competing Species 11 Series Solutions to Differential Equations 11.1 Review of Power Series 11.2 Series Solutions Near Ordinary Points 11.3 Legendre's Equation 11.4 Types of singular Points-Euler's Equation 11.5 Series Solutions Near Regular Singular Points 11.6 Series Solutions Near Regular Singular 11.7 Bessel's Equation and Bessel Functions Appendix Complex Numbers and Matrices Answers to Odd-Numbered Problems Index

David Arnold was Assistant Professor of Business Administration at the Harvard Business School and head of its International Marketing Management course. Now an independent consultant and educator, he specializes in international marketing, branding, market analysis, and strategy formulation. His innovative recent work has appeared in Harvard Business Review, Journal of International Business Studies, Sloan Management Review, California Management Review, and the Marketing Science Institute working paper series. He has served as visiting or resident faculty member at leading business schools in Great Britain, Japan, Switzerland, Spain, Argentina, Finland, India, and Pakistan. Arnold's previous book, The Handbook of Brand Management, has been published in 10 languages. 

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