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Differential Equations : Computing and Modeling,9780130797797
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Differential Equations : Computing and Modeling

by ;
Edition:
2nd
ISBN13:

9780130797797

ISBN10:
0130797790
Format:
Hardcover
Pub. Date:
7/1/1999
Publisher(s):
Prentice Hall
List Price: $110.00
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Summary

For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course while maintaining the solid foundation of algebraic techniques that are still essential to science and engineering students. It reflects the new excitement in differential equations as the availability of technical computing environments likeMaple, Mathematica, and MATLAB reshape the role and applications of the discipline. New technology has motivated a shift in emphasis from traditional, manual methods to both qualitative and computer-based methods that render accessible a wider range of realistic applications. With this in mind, the text augments core skills with conceptual perspectives that students will need for the effective use of differential equations in their subsequent work and study.

Table of Contents

Computing Projects v
Preface vii
First-Order Differential Equations
1(74)
Differential Equations and Mathematical Models
1(9)
Integrals as General and Particular Solutions
10(8)
Direction Fields and Solution Curves
18(12)
Separable Equations and Applications
30(14)
Linear First-Order Equations
44(14)
Substitution Methods and Exact Equations
58(17)
Mathematical Models and Numerical Methods
75(65)
Population Models
75(13)
Equilibrium Solutions and Stability
88(6)
Acceleration-Velocity Models
94(11)
Numerical Approximation: Euler's Method
105(11)
A Closer Look at the Euler Method
116(12)
The Runge-Kutta Method
128(12)
Linear Equations of Higher Order
140(102)
Introduction: Second-Order Linear Equations
140(14)
General Solutions of Linear Equations
154(14)
Homogeneous Equations with Constant Coefficients
168(12)
Mechanical Vibrations
180(11)
Nonhomogeneous Equations and the Method of Undetermined Coefficients
191(16)
Forced Oscillations and Resonance
207(13)
Electrical Circuits
220(8)
Endpoint Problems and Eigenvalues
228(14)
Introduction to Systems of Differential Equations
242(42)
First-Order Systems and Applications
242(14)
The Method of Elimination
256(11)
Numerical Methods for Systems
267(17)
Linear Systems of Differential Equations
284(91)
Matrices and Linear Systems
284(20)
The Eigenvalue Method for Homogeneous Systems
304(16)
Second-Order Systems and Mechanical Applications
320(14)
Multiple Eigenvalue Solutions
334(18)
Matrix Exponentials and Linear Systems
352(14)
Nonhomogeneous Linear Systems
366(9)
Nonlinear Systems and Phenomena
375(70)
Stability and the Phase Plane
375(13)
Linear and Almost Linear Systems
388(15)
Ecological Models: Predators and Competitors
403(13)
Nonlinear Mechanical Systems
416(16)
Chaos in Dynamical Systems
432(13)
Laplace Transform Methods
445(67)
Laplace Transforms and Inverse Transforms
445(12)
Transformation of Initial Value Problems
457(12)
Translation and Partial Fractions
469(10)
Derivatives, Integrals, and Products of Transforms
479(9)
Periodic and Piecewise Continuous Input Functions
488(13)
Impulses and Delta Functions
501(11)
References for Further Study 512(2)
Appendix: Existence and Uniqueness of Solutions 514(16)
Answers to Selected Problems 530
Index 1


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