Differential Equations A Modeling Approach

ISBN-10: 0072422297
ISBN-13: 9780072422290
Edition: 2005
Authors: Glenn Ledder
List price: $148.44
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Book details

List price: $148.44
Copyright year: 2005
Publisher: McGraw-Hill Higher Education
Publication date: 7/17/2004
Binding: Hardcover
Pages: 688
Size: 8.25" wide x 9.25" long x 1.25" tall
Weight: 2.838
Language: English

Introduction
Natural Decay and Natural Growth
Differential Equations and Solutions
Mathematical Models and Mathematical Modeling
Scientific Detection of Art Forgery
Basic Concepts and Techniques
A Collection of Mathematical Models
Separable First-Order Equations
Slope Fields
Existence of Unique Solutions
Euler's Method
Runge-Kutta Methods
A Successful Volleyball Serve
Homogeneous Linear Equations
Linear Oscillators
Systems of Linear Algebraic Equations
Theory of Homogeneous Linear Equations
Homogeneous Equations with Constant Coefficients
Real Solutions from Complex Characteristic Values
Multiple Solutions for Repeated Characteristic Values
Some Other Homogeneous Linear Equations
How Long Should Jellyfish Hold their Food?
Nonhomogeneous Linear Equations
More on Linear Oscillator Models
General Solutions for Nonhomogeneous Equations
The Method of Undetermined Coefficients
Forced Linear Oscillators
Solving First-Order Linear Equations
Particular Solutions for Second-Order Equations by Variation of Parameters
A Tuning Circuit for a Radio
Autonomous Equations and Systems
Population Models
The Phase Line
The Phase Plane
The Direction Field and Critical Points
Qualitative Analysis
A Self-Limiting Population
Analytical Methods for Systems
Compartment Models
Eigenvalues and Eigenspaces
Linear Trajectories
Homogeneous Systems with Real Eigenvalues
Homogeneous Systems with Complex Eigenvalues
Additional Solutions for Deficient Matrices
Qualitative Behavior of Nonlinear Systems
Invasion by Disease
The Laplace Transform
Piecewise-Continuous Functions
Definition and Properties of the Laplace Transform
Solution of Initial-Value Problems with the Laplace Transform
Piecewise-Continuous and Impulsive Forcing
Convolution and the Impulse Response Function
Growth of a Structured Population
Vibrating Strings: A Focused Introduction to Partial Differential Equations
Transverse Vibration of a String
The General Solution of the Wave Equation
Vibration Modes of a Finite String
Motion of a Plucked String
Fourier Series
Stringed Instruments and Percussion A Some Additional Topics
Using Integrating Factors to Solve First-Order Linear Equations (Chapter 2)
Proof of the Existence and Uniqueness Theorem for First-Order Equations (Chapter 2)
Error in Numerical Methods (Chapter 2)
Power Series Solutions (Chapter 3)
Matrix Functions (Chapter 6)
Nonhomogeneous Linear Systems (Chapter 6)
The One-Dimensional Heat Equation (Chapter 8)
Laplace's Equation (Chapter 8)
Table of Contents provided by Publisher. All Rights Reserved.

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