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Differential Equations A Systems Approach

ISBN-10: 0132113198

ISBN-13: 9780132113199

Edition: 1998

Authors: Jack L. Goldberg, Merle C. Potter

List price: $111.00
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Description:

Appropriate for an introductory undergraduate course in differential equations. Engineers and scientists study differential equations because of its crucial role in the analysis of physical and biological systems. This short text addresses this need by presenting the classical theory from a systems point of view. Besides making system theory the unifying pedagogical take, this text offers an abundance of applications, examples, and problems. For the instructors interested in combining computer solutions to differential equations, there are many problems which ask students to use MATLAB.
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Book details

List price: $111.00
Copyright year: 1998
Publisher: Prentice Hall PTR
Publication date: 7/31/1997
Binding: Hardcover
Pages: 476
Size: 7.50" wide x 9.75" long x 1.00" tall
Weight: 1.980
Language: English

Complex Numbers
Introduction
The Cartesian and Exponential Forms
Roots of Polynomial Equations and Numbers
Matrix Notation and Terminology
The Solution of Simultaneous Equations
The Algebra of Matrices
Matrix Multiplication
The Inverse of a Matrix
The Computation of A-1
Determinants
Linear Independence
First-Order Differential Equations
Preliminaries
Definitions
The First-Order Linear Equation
Applications of First-Order Linear Equations
Nonlinear Equations of First Order
Linear Systems
Introduction
Eigenvalues and Eigenvectors
First-Order Systems
Solution and Fundamental Solution Matrices
Some Fundamental Theorems
Solutions of Nonhomogeneous Systems
Nonhomogeneous Initial-Value Problems
Fundamental Solution Matrices
Second-Order Linear Equations
Introduction
Sectionally Continuous Functions
Linear Differential Operators
Linear Independence and the Wronskian
The Nonhomogeneous Equation
Constant Coefficient Equations
Spring-Mass Systems in Free Motion
The Electric Circuit
Undetermined Coefficients
The Spring-Mass System: Forced Motion
The Cauchy-Euler Equation
Variation of Parameters
Higher Order Equations
Introduction
The Homogeneous Equation
The Nonhomogeneous Equation
Companion Systems
Homogeneous Companion Systems
Variation of Parameters
The Laplace Transform
Introduction
Preliminaries
General Properties of the Laplace Transform
Sectionally Continuous Functions
Laplace Transforms of Periodic Functions
The Inverse Laplace Transform
Partial Fractions
The Convolution Theorem
The Solution of Initial-Value Problems
The Laplace Transform of Systems
Tables of Transforms
Series Methods
Introduction
Analytic Functions
Taylor Series of Analytic Functions
Power Series Solutions
Legendre's Equations
Three Important Examples
Bessel's Equation
The Wronskian Method
The Frobenius Method
Numerical Methods
Introduction
Direction Fields
Notational Conventions
The Euler Method
Heun's Method
Taylor Series Methods
Runge-Kutta Methods
Multivariable Methods
Higher Order Equations
Boundary-Value Problems
Introduction
Separation of Variables
Fourier Series Expansions
The Wave Equation
The One-Dimensional Heat Equation
The Laplace Equation
A Potential about a Spherical Surface