Differential Equations: An Introduction to Modern Methods and Applications, 2nd Edition

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2010-12-01
  • Publisher: Wiley

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Unlike other texts in the market, this second edition presents differential equations consistent with the way scientists and engineers use modern methods in their work. Technology is used freely, with more emphasis on modeling, graphical representation, qualitative concepts, and geometric intuition than on theoretical issues. It also refers to larger-scale computations that computer algebra systems and DE solvers make possible. More exercises and examples involving working with data and devising the model provide scientists and engineers with the tools needed to model complex real-world situations.

Table of Contents

Mathematical Models, Solutions, and Direction Fields
Linear Equations: Method of Integrating Factors
Numerical Approximations: Euler's Method
Classification of Differential Equations
First Order Differential Equations
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
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
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
Mechanical and Electrical Vibrations
Nonhomogeneous Equations: Method of Undetermined Coefficients
Forced Vibrations, Frequency Response, and Resonance
Variation of Parameters
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
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
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
Almost Linear Systems
Competing Species
Predator-Prey Equations
Periodic Solutions and Limit Cycles
Chaos and Strange Attractors: The Lorenz Equations
Modeling of Epidemics
Harvesting in a Competitive Environment
The Rossler System
[Chapters 8-10 in Boundary Value Problems version only]
Series Solutions of Second Order Equations
Review of Power Systems
Series Solutions Near an Ordinary Point, Part I
Series Solutions Near an Ordinary Point, Part II
Regular Singular Points
Series Solutions Near a Regular Singular Point, Part I
Series Solutions Near a Regular Singular Point, Part II
Bessel's Equation
Distraction Through a Circular Aperture
Hermite Polynomials and the Quantum Mechanical Harmonic Oscillator
Perturbation Methods
Partial Differential Equations and Fourier Series
Two-Point Boundary Value Problems
Fourier Series
The Fourier Convergence Theorem
Even and Odd Functions
Separation of Variables, Heat Conduction in a Rod
Other Heat Conduction Problems
The Wave Equation, Vibrations of an Elastic String
Laplace's Equation
Estimating the Diffusion Coefficient in the Heat Equation
The Transmission Line Problem
Solving Poisson's Equation by Finite Differences
Matrices and Linear Algebra
Systems of Linear Algebraic Equations, Linear Independence, and Rank
Determinants and Inverses
The Eigenvalue Problem
Complex Variables
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