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Elementary Differential Equations With Boundary Value Problems,9780130113016
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Elementary Differential Equations With Boundary Value Problems

by ;
Edition:
4th
ISBN13:

9780130113016

ISBN10:
0130113018
Format:
Hardcover
Pub. Date:
10/1/1999
Publisher(s):
PRENTICE HALL
List Price: $111.35

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This is the 4th edition with a publication date of 10/1/1999.
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Summary

For courses in differential equations. This book, with enough material for 2 terms, provides a concrete and readable text for the traditional course in elementary differential equations that science, engineering, and mathematics students take following calculus. This is a strongly algebraic-oriented text with some computer enhancements for numerical methods. Matters of definition, classification, and logical structure deserve (and receive here) careful attention for the first time in the mathematical experience of many of the students. While it is neither feasible nor desirable to include proofs of the fundamental existence and uniqueness theorems along the way in an elementary course, students need to see precise and clear-cut statements of these theorems, and understand their role in the subject. Appropriate existence and uniqueness proofs in the Appendix are included, and referred to where appropriate in the main body of the text.

Table of Contents

Preface ix
First-Order Differential Equations
1(93)
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(13)
Linear First-Order Equations
43(13)
Substitution Methods and Exact Equations
56(14)
Population Models
70(11)
Acceleration-Velocity Models
81(13)
Linear Equations of Higher Order
94(97)
Introduction: Second-Order Linear Equations
94(15)
General Solutions of Linear Equations
109(12)
Homogeneous Equations with Constant Coefficients
121(11)
Mechanical Vibrations
132(12)
Undetermined Coefficients and Variation of Parameters
144(14)
Forced Oscillations and Resonance
158(12)
Electrical Circuits
170(7)
Endpoint Problems and Eigenvalues
177(14)
Power Series Methods
191(72)
Introduction and Review of Power Series
191(14)
Series Solutions Near Ordinary Points
205(11)
Regular Singular Points
216(15)
Method of Frobenius: The Exceptional Cases
231(16)
Bessel's Equation
247(10)
Applications of Bessel Functions
257(6)
Laplace Transform Methods
263(61)
Laplace Transforms and Inverse Transforms
263(11)
Transformation of Initial Value Problems
274(9)
Translation and Partial Fractions
283(9)
Derivatives, Integrals, and Products of Transforms
292(8)
Periodic and Piecewise Continuous Input Functions
300(13)
Impulses and Delta Functions
313(11)
Linear Systems of Differential Equations
324(111)
First-Order Systems and Applications
324(14)
The Method of Elimination
338(10)
Matrices and Linear Systems
348(20)
The Eigenvalue Method for Homogeneous Systems
368(16)
Second-Order Systems and Mechanical Applications
384(13)
Multiple Eigenvalue Solutions
397(16)
Matrix Exponentials and Linear Systems
413(13)
Nonhomogeneous Linear Systems
426(9)
Numerical Methods
435(51)
Numerical Approximation: Euler's Method
435(11)
A Closer Look at the Euler Method
446(11)
The Runge-Kutta Method
457(12)
Numerical Methods for Systems
469(17)
Nonlinear Systems and Phenomena
486(72)
Equilibrium Solutions and Stability
486(7)
Stability and the Phase Plane
493(13)
Linear and Almost Linear Systems
506(13)
Ecological Models: Predators and Competitors
519(13)
Nonlinear Mechanical Systems
532(13)
Chaos in Dynamical Systems
545(13)
Fourier Series Methods
558(74)
Periodic Functions and Trigonometric Series
558(9)
General Fourier Series and Convergence
567(8)
Fourier Sine and Cosine Series
575(11)
Applications of Fourier Series
586(6)
Heat Conduction and Separation of Variables
592(16)
Vibrating Strings and the One-Dimensional Wave Equation
608(13)
Steady-State Temperature and Laplace's Equation
621(11)
Eigenvalues and Boundary Value Problems
632(66)
Sturm-Liouville Problems and Eigenfunction Expansions
632(12)
Applications of Eigenfunction Series
644(11)
Steady Periodic Solutions and Natural Frequencies
655(8)
Cylindrical Coordinate Problems
663(15)
Higher-Dimensional Phenomena
678(20)
References for Further Study 698(2)
Appendix: Existence and Uniqueness of Solutions 700(16)
Answers to Selected Problems 716(21)
Index 737


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