Differential Equations 2E an Introduction to Modern Methods and Applications with Boundary Value Problems

The modern landscape of technology and industry demands an equally modern approach to differential equations in the classroom. Designed for a first course in differential equations, the second edition of Brannan/Boyce's Differential Equations: An Introduction to Modern Methods and Applications is consistent with the way engineers and scientists use mathematics in their daily work. The focus on fundamental skills, careful application of technology, and practice in modeling complex systems prepares students for the realities of the new millennium, providing the building blocks to be successful problem-solvers in today's workplace. The text emphasizes a systems approach to the subject and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. WileyPLUS sold separately from text.

Table of Contents:
1 Introduction 1.1 Mathematical Models, Solutions, and Direction Fields 1.2 Linear Equations: Method of Integrating Factors 1.3 Numerical Approximations: Euler's Method 1.4 Classification of Differential Equations 2 First Order Differential Equations 2.1 Separable Equations 2.2 Modeling with First Order Equations 2.3 Differences between Linear and Nonlinear Equations 2.4 Autonomous Equations and Population Dynamics 2.5 Exact Equations and Integrating Factors 2.6 Accuracy of Numerical Methods 2.7 Improved Euler and Runge-Kutta Methods Projects 2.P.1 Harvesting a Renewable Resource 2.P.3 Designing a Drip Dispenser for a Hydrology Experiment 2.P.4 A Mathematical Model of a Groundwater Contaminant Source 2.P.5 Monte-Carlo Option Pricing: Pricing Financial Options by Flipping a Coin 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 3.7 Numerical Methods for Systems of First Order Equations Projects 3.P.1 Eigenvalue Placement Design of a Satellite Attitude Control System 3.P.2 Estimating Rate Constants for an Open Two-Compartment Model 3.P.3 The Ray Theory of Wave Propagation 3.P.4 A Blood-Brain Pharmacokinetic Model 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 Uniformly Distributing Points on a Sphere 4.P.5 Euler-Lagrange Equations 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 Effects of Pole Locations on Step Responses of Second Order Systems 5.P.3 The Watt Governor, Feedback Control, and Stability 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 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 A Compartment Model of Heat Flow in a Rod 6.P.2 Earthquakes and Tall Buildings 6.P.3 Controlling a Spring-Mass System to Equilibrium 7 Nonlinear Differential Equations and Stability 7.1 Almost Linear Systems 7.2 Competing Species 7.3 Predator-Prey Equations 7.4 Periodic Solutions and Limit Cycles 7.5 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 [Chapters 8-10 in Boundary Value Problems version only] 8 Series Solutions of Second Order Equations 8.1 Review of Power Systems 8.2 Series Solutions Near an Ordinary Point, Part I 8.3 Series Solutions Near an Ordinary Point, Part II 8.4 Regular Singular Points 8.5 Series Solutions Near a Regular Singular Point, Part I 8.6 Series Solutions Near a Regular Singular Point, Part II 8.7 Bessel's Equation Projects 8.P.1 Distraction Through a Circular Aperture 8.P.2 Hermite Polynomials and the Quantum Mechanical Harmonic Oscillator 8.P.3 Perturbation Methods 9 Partial Differential Equations and Fourier Series 9.1 Two-Point Boundary Value Problems 9.2 Fourier Series 9.3 The Fourier Convergence Theorem 9.4 Even and Odd Functions 9.5 Separation of Variables, Heat Conduction in a Rod 9.6 Other Heat Conduction Problems 9.7 The Wave Equation, Vibrations of an Elastic String 9.8 Laplace's Equation Projects 9.P.1 Estimating the Diffusion Coefficient in the Heat Equation 9.P.2 The Transmission Line Problem 9.P.3 Solving Poisson's Equation by Finite Differences 10 Boundary Value Problems and Sturm-Liouville Theory 10.1 The Occurrence of Two-Point Boundary Value Problems 10.2 Sturm-Liouville Boundary Value Problems 10.3 Nonhomogeneous Boundary Value Problems 10.4 Singular Sturm-Liouville Problems 10.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion 10.6 Series of Orthogonal Functions: Mean Convergence Projects 10.P.1 Dynamic Behavior of a Hanging Cable 10.P.2 Advection-Dispersion: A Model for Solute Transport in Saturated Porous Media 10.P.3 Fisher's Equation for Population Growth and Dispersion A Matrices and Linear Algebra A.1 Matrices A.2 Systems of Linear Algebraic Equations, Linear Independence, and Rank A.3 Determinants and Inverses A.4 The Eigenvalue Problem B Complex Variables