- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
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.
Contents
1 Introduction 1.1 Mathematical Models, Solutions, and Direction Fields1.2 Linear Equations: Method of Integrating Factors1.3 Numerical Approximations: Euler's Method1.4 Classification of Differential Equations2 First Order Differential Equations2.1 Separable Equations2.2 Modeling with First Order Equations2.3 Differences between Linear and Nonlinear Equations2.4 Autonomous Equations and Population Dynamics2.5 Exact Equations and Integrating Factors2.6 Accuracy of Numerical Methods2.7 Improved Euler and Runge-Kutta MethodsProjects2.P.1 Harvesting a Renewable Resource2.P.3 Designing a Drip Dispenser for a Hydrology Experiment2.P.4 A Mathematical Model of a Groundwater Contaminant Source2.P.5 Monte-Carlo Option Pricing: Pricing Financial Options by Flipping a Coin3 Systems of Two First Order Equations3.1 Systems of Two Linear Algebraic Equations3.2 Systems of Two First Order Linear Differential Equations3.3 Homogeneous Linear Systems with Constant Coefficients3.4 Complex Eigenvalues3.5 Repeated Eigenvalues3.6 A Brief Introduction to Nonlinear Systems3.7 Numerical Methods for Systems of First Order EquationsProjects3.P.1 Eigenvalue Placement Design of a Satellite Attitude Control System3.P.2 Estimating Rate Constants for an Open Two-Compartment Model3.P.3 The Ray Theory of Wave Propagation3.P.4 A Blood-Brain Pharmacokinetic Model4 Second Order Linear Equations4.1 Definitions and Examples4.2 Theory of Second Order Linear Homogeneous Equations4.3 Linear Homogeneous Equations with Constant Coefficients4.4 Mechanical and Electrical Vibrations4.5 Nonhomogeneous Equations: Method of Undetermined Coefficients4.6 Forced Vibrations, Frequency Response, and Resonance4.7 Variation of ParametersProjects4.P.1 A Vibration Insulation Problem4.P.2 Linearization of a Nonlinear Mechanical System4.P.3 A Spring-Mass Event Problem4.P.4 Uniformly Distributing Points on a Sphere4.P.5 Euler-Lagrange Equations5 The Laplace Transform5.1 Definition of the Laplace Transform5.2 Properties of the Laplace Transform5.3 The Inverse Laplace Transform5.4 Solving Differential Equations with Laplace Transforms5.5 Discontinuous Functions and Periodic Functions5.6 Differential Equations with Discontinuous Forcing Functions5.7 Impulse Functions5.8 Convolution Integrals and Their Applications5.9 Linear Systems and Feedback ControlProjects5.P.1 An Electric Circuit Problem5.P.2 Effects of Pole Locations on Step Responses of Second Order Systems5.P.3 The Watt Governor, Feedback Control, and Stability6 Systems of First Order Linear Equations6.1 Definitions and Examples6.2 Basic Theory of First Order Linear Systems6.3 Homogeneous Linear Systems with Constant Coefficients6.4 Complex Eigenvalues6.5 Fundamental Matrices and the Exponential of a Matrix6.6 Nonhomogeneous Linear Systems6.7 Defective MatricesProjects6.P.1 A Compartment Model of Heat Flow in a Rod6.P.2 Earthquakes and Tall Buildings6.P.3 Controlling a Spring-Mass System to Equilibrium7 Nonlinear Differential Equations and Stability7.1 Almost Linear Systems7.2 Competing Species7.3 Predator-Prey Equations7.4 Periodic Solutions and Limit Cycles7.5 Chaos and Strange Attractors: The Lorenz EquationsProjects7.P.1 Modeling of Epidemics7.P.2 Harvesting in a Competitive Environment7.P.3 The Rossler System[Chapters 8-10 in Boundary Value Problems version only]8 Series Solutions of Second Order Equations8.1 Review of Power Systems8.2 Series Solutions Near an Ordinary Point, Part I8.3 Series Solutions Near an Ordinary Point, Part II8.4 Regular Singular Points8.5 Series Solutions Near a Regular Singular Point, Part I8.6 Series Solutions Near a Regular Singular Point, Part II8.7 Bessel's EquationProjects8.P.1 Distraction Through a Circular Aperture8.P.2 Hermite Polynomials and the Quantum Mechanical Harmonic Oscillator8.P.3 Perturbation Methods9 Partial Differential Equations and Fourier Series9.1 Two-Point Boundary Value Problems9.2 Fourier Series9.3 The Fourier Convergence Theorem9.4 Even and Odd Functions9.5 Separation of Variables, Heat Conduction in a Rod9.6 Other Heat Conduction Problems9.7 The Wave Equation, Vibrations of an Elastic String9.8 Laplace's EquationProjects9.P.1 Estimating the Diffusion Coefficient in the Heat Equation9.P.2 The Transmission Line Problem9.P.3 Solving Poisson's Equation by Finite Differences10 Boundary Value Problems and Sturm-Liouville Theory10.1 The Occurrence of Two-Point Boundary Value Problems10.2 Sturm-Liouville Boundary Value Problems10.3 Nonhomogeneous Boundary Value Problems10.4 Singular Sturm-Liouville Problems10.5 Further Remarks on the Method of Separation of Variables: A Bessel SeriesExpansion10.6 Series of Orthogonal Functions: Mean ConvergenceProjects10.P.1 Dynamic Behavior of a Hanging Cable10.P.2 Advection-Dispersion: A Model for Solute Transport in Saturated Porous Media10.P.3 Fisher's Equation for Population Growth and DispersionA Matrices and Linear AlgebraA.1 MatricesA.2 Systems of Linear Algebraic Equations, Linear Independence, and RankA.3 Determinants and InversesA.4 The Eigenvalue ProblemB Complex Variables
