Differential Equations

An Introduction to Modern Methods and Applications, EMEA Edition

Häftad, Engelska, 2019

Av James R. Brannan, William E. Boyce, James R. (Clemson University) Brannan, William E. (Rensselaer Polytechnic Institute) Boyce

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Differential Equations: An Introduction to Modern Methods and Applications, 3rd Edition is consistent with the way engineers and scientists use mathematics in their daily work. 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. 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. Section exercises throughout the text provide hands-on experience in modeling, analysis, and computer experimentation. Projects at the end of each chapter provide additional opportunities for students to explore the role played by differential equations in the sciences and engineering.

Produktinformation

Utgivningsdatum2019-11-21
Mått10 x 10 x 10 mm
Vikt454 g
FormatHäftad
SpråkEngelska
Antal sidor696
Upplaga3
FörlagJohn Wiley & Sons Inc
ISBN9781119657637

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Chapter 1 Introduction 11.1 Mathematical Models and Solutions 21.2 Qualitative Methods: Phase Lines and Direction Fields 121.3 Definitions, Classification, and Terminology 28Chapter 2 First Order Differential Equations 372.1 Separable Equations 382.2 Linear Equations: Method of Integrating Factors 452.3 Modeling with First Order Equations 552.4 Differences Between Linear and Nonlinear Equations 702.5 Autonomous Equations and Population Dynamics 802.6 Exact Equations and Integrating Factors 932.7 Substitution Methods 101Projects2.P.1 Harvesting a Renewable Resource 1102.P.2 A Mathematical Model of a Groundwater Contaminant Source 1112.P.3 Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin 113Chapter 3 Systems of Two First Order Equations 1163.1 Systems of Two Linear Algebraic Equations 1173.2 Systems of Two First Order Linear Differential Equations 1293.3 Homogeneous Linear Systems with Constant Coefficients 1453.4 Complex Eigenvalues 1673.5 Repeated Eigenvalues 1783.6 A Brief Introduction to Nonlinear Systems 189Projects3.P.1 Estimating Rate Constants for an Open Two-Compartment Model 1993.P.2 A Blood–Brain Pharmacokinetic Model 201Chapter 4 Second Order Linear Equations 2034.1 Definitions and Examples 2034.2 Theory of Second Order Linear Homogeneous Equations 2164.3 Linear Homogeneous Equations with Constant Coefficients 2284.4 Mechanical and Electrical Vibrations 2414.5 Nonhomogeneous Equations; Method of Undetermined Coefficients 2524.6 Forced Vibrations, Frequency Response, and Resonance 2614.7 Variation of Parameters 274Projects4.P.1 A Vibration Insulation Problem 2854.P.2 Linearization of a Nonlinear Mechanical System 2864.P.3 A Spring-Mass Event Problem 2884.P.4 Euler–Lagrange Equations 289Chapter 5 The Laplace Transform 2945.1 Definition of the Laplace Transform 2955.2 Properties of the Laplace Transform 3045.3 The Inverse Laplace Transform 3115.4 Solving Differential Equations with Laplace Transforms 3205.5 Discontinuous Functions and Periodic Functions 3285.6 Differential Equations with Discontinuous Forcing Functions 3375.7 Impulse Functions 3445.8 Convolution Integrals and Their Applications 3515.9 Linear Systems and Feedback Control 361Projects5.P.1 An Electric Circuit Problem 3715.P.2 The Watt Governor, Feedback Control, and Stability 372Chapter 6 Systems of First Order Linear Equations 3776.1 Definitions and Examples 3786.2 Basic Theory of First Order Linear Systems 3896.3 Homogeneous Linear Systems with Constant Coefficients 3996.4 Nondefective Matrices with Complex Eigenvalues 4106.5 Fundamental Matrices and the Exponential of a Matrix 4206.6 Nonhomogeneous Linear Systems 4316.7 Defective Matrices 438Projects6.P.1 Earthquakes and Tall Buildings 4466.P.2 Controlling a Spring-Mass System to Equilibrium 449Chapter 7 Nonlinear Differential Equations and Stability 4567.1 Autonomous Systems and Stability 4567.2 Almost Linear Systems 4667.3 Competing Species 4767.4 Predator–Prey Equations 4887.5 Periodic Solutions and Limit Cycles 4967.6 Chaos and Strange Attractors: The Lorenz Equations 506Projects7.P.1 Modeling of Epidemics 5147.P.2 Harvesting in a Competitive Environment 5167.P.3 The R¨ossler System 518Chapter 8 Numerical Methods 5198.1 Numerical Approximations: Euler’s Method 5198.2 Accuracy of Numerical Methods 5308.3 Improved Euler and Runge–Kutta Methods 5378.4 Numerical Methods for Systems of First Order Equations 546Projects8.P.1 Designing a Drip Dispenser for a Hydrology Experiment 5508.P.2 Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin 551Chapter 9 Series Solutions of Second Order Equations (online only)9.1 Review of Power Series9.2 Series Solutions Near an Ordinary Point, Part I9.3 Series Solutions Near an Ordinary Point, Part II9.4 Regular Singular Points9.5 Series Solutions Near a Regular Singular Point, Part I9.6 Series Solutions Near a Regular Singular Point, Part II9.7 Bessel’s EquationProjects9.P.1 Diffraction Through a Circular Aperature9.P.2 Hermite Polynomials and the Quantum Mechanical Harmonic Oscillator9.P.3 Perturbation MethodsChapter 10 Orthogonal Functions, Fourier Series, and Boundary Value Problems (online only)10.1 Orthogonal Families in the Space PC[a, b]10.2 Fourier Series10.3 Elementary Two-Point Boundary Value Problems10.4 General Sturm–Liouville Boundary Value Problems10.5 Generalized Fourier Series and Eigenfunction Expansions10.6 Singular Boundary Value Problems10.7 Convergence IssuesChapter 11 Elementary Partial Differential Equations (online only)11.1 Terminology11.2 Heat Conduction in a Rod—Homogeneous Case11.3 Heat Conduction in a Rod—Nonhomogeneous Case11.4 Wave Equation—Vibrations of an Elastic String11.5 Wave Equation—Vibrations of a Circular Membrane11.6 Laplace EquationProjects11.P.1 Estimating the Diffusion Coefficient in the Heat Equation11.P.2 The Transmission Line Problem11.P.3 Solving Poisson’s Equation by Finite Differences11.P.4 Dynamic Behavior of a Hanging Cable11.P.5 Advection Dispersion: A Model for Solute Transport in Saturated Porous Media11.P.6 Fisher’s Equation for Population Growth and DispersionAppendices (available on companion web site)11.A Derivation of the Heat Equation11.B Derivation of the Wave EquationAppendix A Matrices and Linear Algebra 555A.1 Matrices 555A.2 Systems of Linear Algebraic Equations, Linear Independence, and Rank 564A.3 Determinants and Inverses 581A.4 The Eigenvalue Problem 590Appendix B Complex Variables (online only)Review of Integration (online only)Answers 601References 664Index 666