Differential Equations An Introduction to Modern Methods and Applications

ISBN-10: 0471651419
ISBN-13: 9780471651413
Edition: 11th 2007
List price: $230.95 Buy it from $1.40
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Description: Differential Equations: An Introduction to Modern Methods and Applications is a textbook designed for a first course in differential equations commonly taken by undergraduates majoring in engineering or science. It emphasizes a systems approach to  More...

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Book details

List price: $230.95
Edition: 11th
Copyright year: 2007
Publisher: John Wiley & Sons, Incorporated
Publication date: 12/13/2006
Binding: Hardcover
Pages: 704
Size: 8.50" wide x 10.25" long x 1.25" tall
Weight: 3.036
Language: English

Differential Equations: An Introduction to Modern Methods and Applications is a textbook designed for a first course in differential equations commonly taken by undergraduates majoring in engineering or science. It 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. Section exercises throughout the text are designed to give students hands-on experience in modeling, analysis, and computer experimentation. Optional projects at the end of each chapter provide additional opportunitites for students to explore the role played by differential equations in scientific and engineering problems of a more serious nature.

Introduction
Some Basic Mathematical Models
Direction Fields
Solutions of Some Differential Equations
Numerical Approximations: Euler's Method
Classification of Differential Equations
First Order Differential Equations
Linear Equations
Method of Integrating Factors
Separable Equations
Modeling with First Order Equations
Differences Between Linear and Nonlinear Equations
Autonomous Equations and Population Dynamics
Exact Equations and Integrating Factors
Accuracy of Numerical Methods
Improved Euler and Runge-Kutta Methods
Summary
Projects
Harvesting a Renewable Resource
Designing a Drip Dispenser for a Hydrology Experiment
A Mathematical Model of a Groundwater Contaminant Source
Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin
Systems of Two First Order Equations
Systems of Two Linear Algebraic Equations
Systems of Two First Order Linear Differential Equations
Homogeneous Linear Systems with Constant Coefficients
Complex Eigenvalues
Repeated Eigenvalues
A Brief Introduction to Nonlinear Systems
Numerical Methods for Systems of First Order Equations
Summary
Projects
Eigenvalue-Placement Design of a Satellite Attitude Control System
Estimating Rate Constants for an Open Two-Compartment Model
The Ray Theory of Wave Propagation
A Blood-Brain Pharmacokinetic Model
Second Order Linear Equations
Definitions and Examples
Theory of Second Order Linear Homogeneous Equations
Linear Homogeneous Equations with Constant Coefficients
Characteristic Equations with Complex Roots
Mechanical and Electrical Vibrations
Nonhomogeneous Equations
Method of Undetermined Coefficients
Forced Vibrations, Frequency Response, and Resonance
Variation of Parameters
Summary
Projects
A Vibration Insulation Problem
Linearization of a Nonlinear Mechanical System
A Spring-Mass Event Problem
Uniformly Distributing Points on a Sphere
Euler-Lagrange Equations
The Laplace Transform
Definition of the Laplace Transform
Properties of the Laplace Transform
The Inverse Laplace Transform
Solving Differential Equations with Laplace Transforms
Discontinuous Functions and Periodic Functions
Differential Equations with Discontinuous Forcing Functions
Impulse Functions
Convolution Integrals and Their Applications
Linear Systems and Feedback Control
Summary
Projects
An Electric Circuit Problem
Effects of Pole Locations on Step Responses of Second Order Systems
The Watt Governor, Feedback Control, and Stability
Systems of First Order Linear Equations
Definitions and Examples
Basic Theory of First Order Linear Systems
Homogeneous Linear Systems with Constant Coefficients
Complex Eigenvalues
Fundamental Matrices and the Exponential of a Matrix
Nonhomogeneous Linear Systems
Defective Matrices
Summary
Projects
A Compartment Model of Heat Flow in a Rod
Earthquakes and Tall Buildings
Controlling a Spring-Mass System to Equilibrium
Nonlinear Differential Equations and Stability
Autonomous Systems and Stability
Almost Linear Systems
Competing Species
Predator-Prey E

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