Differential Equations: An Introduction to Modern Methods and Applications 3e with WileyPLUS Blackboard Card Set

Table of Contents:
Chapter 1: Introduction 1.1 Mathematical Models and Solutions 1.2 Qualitative Methods: Phase Lines and Direction Fields 1.3 Definitions, Classification, and Terminology Chapter 2: First Order Differential Equations 2.1 Separable Equations 2.2 Linear Equations: Method of Integrating Factors 2.3 Modeling with First Order Equations 2.4 Differences Between Linear and Nonlinear Equations 2.5 Autonomous Equations and Population Dynamics 2.6 Exact Equations and Integrating Factors 2.7 Substitution Methods Projects 2.P.1 Harvesting a Renewable Resource 2.P.2 A Mathematical Model of a Groundwater Contaminant Source 2.P.3 Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin Chapter 3: Systems of Two First Order Equations 3.1 Systems of Two Linear Algebraic Equations 3.2 Systems of Two First Order Linear Differential Equations 3.3 Homogeneous Linear Systems with Constant Coefficients 3.4 Complex Eigenvalues 3.5 Repeated Eigenvalues 3.6 A Brief Introduction to Nonlinear Systems Projects 3.P.1 Estimating Rate Constants for an Open Two-Compartment Model 3.P.2 A Blood-Brain Pharmacokinetic Model Chapter 4: Second Order Linear Equations 4.1 Definitions and Examples 4.2 Theory of Second Order Linear Homogeneous Equations 4.3 Linear Homogeneous Equations with Constant Coefficients 4.4 Mechanical and Electrical Vibrations 4.5 Nonhomogeneous Equations; Method of Undetermined Coefficients 4.6 Forced Vibrations, Frequency Response, and Resonance 4.7 Variation of Parameters Projects 4.P.1 A Vibration Insulation Problem 4.P.2 Linearization of a Nonlinear Mechanical System 4.P.3 A Spring-Mass Event Problem 4.P.4 Euler-Lagrange Equations Chapter 5: The Laplace Transform 5.1 Definition of the Laplace Transform 5.2 Properties of the Laplace Transform 5.3 The Inverse Laplace Transform 5.4 Solving Differential Equations with Laplace Transforms 5.5 Discontinuous Functions and Periodic Functions 5.6 Differential Equations with Discontinuous Forcing Functions 5.7 Impulse Functions 5.8 Convolution Integrals and Their Applications 5.9 Linear Systems and Feedback Control Projects 5.P.1 An Electric Circuit Problem 5.P.2 The Watt Governor, Feedback Control, and Stability Chapter 6: Systems of First Order Linear Equations 6.1 Definitions and Examples 6.2 Basic Theory of First Order Linear Systems 6.3 Homogeneous Linear Systems with Constant Coefficients 6.4 Nondefective Matrices with Complex Eigenvalues 6.5 Fundamental Matrices and the Exponential of a Matrix 6.6 Nonhomogeneous Linear Systems 6.7 Defective Matrices Projects 6.P.1 Earthquakes and Tall Buildings 6.P.2 Controlling a Spring-Mass System to Equilibrium Chapter 7: Nonlinear Differential Equations and Stability 7.1 Autonomous Systems and Stability 7.2 Almost Linear Systems 7.3 Competing Species 7.4 Predator-Prey Equations 7.5 Periodic Solutions and Limit Cycles 7.6 Chaos and Strange Attractors: The Lorenz Equations Projects 7.P.1 Modeling of Epidemics 7.P.2 Harvesting in a Competitive Environment 7.P.3 The Rossler System Chapter 8: Numerical Methods 8.1 Numerical Approximations: Euler’s Method 8.2 Accuracy of Numerical Methods 8.3 Improved Euler and Runge-Kutta Methods 8.4 Numerical Methods for Systems of First Order Equations Projects 8.P.1 Designing a Drip Dispenser for a Hydrology Experiment 8.P.2 Monte Carlo Option Pricing: Pricing Financial Option by Flipping a Coin Chapter 9: Series Solutions of Second order Equations 9.1 Review of Power Series 9.2 Series Solutions Near an Ordinary Point, Part I 9.3 Series Solutions Near an Ordinary Point, Part II 9.4 Regular Singular Points 9.5 Series Solutions Near a Regular Singular Point, Part I 9.6 Series Solutions Near a Regular Singular Point, Part II 9.7 Bessel’s Equation Projects 9.P.1 Diffraction Through a Circular Aperature 9.P.2 Hermite Polynomials and the Quantum Mechanical Harmonic Oscillator 9.P.3 Perturbation Methods Chapter 10: Orthogonal Functions, Fourier Series and Boundary-Value Problems 10.1 Orthogonal Families in the Space PC [a,b] 10.2 Fourier Series 10.3 Elementary Two-Point Boundary Value Problems 10.4 General Sturm-Liouville Boundary Value Problems 10.5 Generalized Fourier Series and Eigenfunction Expansions 10.6 Singular Boundary Value Problems 10.7 Convergence Issues Chapter 11: Elementary Partial Differential Equations 11.1 Terminology 11.2 Heat Conduction in a Rod—Homogeneous Case 11.3 Heat Conduction in a Rod—Nonhomogeneous Case 11.4 Wave Equation—Vibrations of an Elastic String 11.5 Wave Equation—Vibrations of a Circular Membrane 11.6 Laplace Equation Projects 11.P.1 Estimating the Diffusion Coefficient in the Heat Equation 11.P.2 The Transmission Line Problem 11.P.3 Solving Poisson’s Equation by Finite Differences 11.P.4 Dynamic Behavior of a Hanging Cable 11.P.5 Advection Dispersion: A Model for Solute Transport in Saturated Porous Media 11.P.6 Fisher’s Equation for Population Growth and Dispersion Appendices 11.A Derivation of the Heat Equation 11.B Derivation of the Wave Equation A: Matrices and Linear Algebra A.1 Matrices A.2 Systems of Linear Algebraic Equations, Linear Independence, and Rank A.3 Determinates and Inverses A.4 The Eigenvalue Problem B: Complex Variables Answers to Selected Problems References Index