Fundamentals of Differential Equations,9780201338683

Fundamentals of Differential Equations

by ; ;
Edition: 5th
ISBN13: 9780201338683
ISBN10: 0201338688
Format: Hardcover w/CD
Pub. Date: 2000-01-01
Publisher(s): Addison Wesley
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Summary

This text is in a flexible one-semester text that spans a variety of topics in the basic theory as well as applications of differential equations.

Table of Contents

Introduction
1(41)
Background
1(5)
Solutions and Initial Value Problems
6(10)
Direction Fields
16(8)
The Phase Line
24(7)
The Approximation Method of Euler
31(11)
Chapter Summary
37(1)
Technical Writing Exercises
37(1)
Group Projects for Chapter 1
38(1)
Taylor Series Method
38(1)
Picard's Method
39(1)
Magnetic Dipole
40(2)
First Order Differential Equations
42(51)
Introduction: Motion of a Falling Body
42(3)
Separable Equations
45(9)
Linear Equations
54(9)
Exact Equations
63(10)
Special Integrating Factors
73(4)
Substitutions and Transformations
77(16)
Chapter Summary
86(1)
Review Problems
87(1)
Technical Writing Exercises
88(1)
Group Projects for Chapter 2
89(1)
The Snowplow Problem
89(1)
Two Snowplows
89(1)
Asymptotic Behavior of Solutions to Linear Equations
90(1)
Torricelli's Law of Fluid Flow
90(2)
Clairaut Equations and Singular Solutions
92(1)
Mathematical Models and Numerical Methods Involving First Order Equations
93(63)
Mathematical Modeling
93(2)
Compartmental Analysis
95(12)
Heating and Cooling of Buildings
107(7)
Newtonian Mechanics
114(10)
Improved Euler's Method
124(11)
Higher-Order Numerical Methods: Taylor and Runge-Kutta
135(9)
Professional Codes for Solving Initial Value Problems
144(12)
Group Projects for Chapter 3
148(1)
Delay Differential Equations
148(1)
Aquaculture
149(1)
Curve of Pursuit
150(1)
Aircraft Guidance in a Crosswind
151(1)
Stability of Numerical Methods
152(1)
Period Doubling and Chaos
153(2)
Bang-Bang Controls
155(1)
Linear Second Order Equations
156(105)
Introduction: The Mass-Spring Oscillator
156(5)
Linear Differential Operators
161(7)
Fundamental Solutions of Homogeneous Equations
168(10)
Reduction of Order
178(5)
Homogeneous Linear Equations with Constant Coefficients
183(8)
Auxiliary Equations with Complex Roots
191(9)
Superposition and Nonhomogeneous Equations
200(4)
Method of Undetermined Coefficients
204(9)
Variation of Parameters
213(5)
Qualitative Considerations for Variable-Coefficient and Nonlinear Equations
218(12)
A Closer Look at Free Mechanical Vibrations
230(10)
A Closer Look at Forced Mechanical Vibrations
240(21)
Chapter Summary
248(2)
Review Problems
250(1)
Technical Writing Exercises
251(1)
Group Projects for Chapter 4
252(1)
Undetermined Coefficients Using Complex Arithmetic
252(1)
An Alternative to the Method of Undetermined Coefficients
253(1)
Convolution Method
254(1)
Linearization of Nonlinear Problems
255(1)
Nonlinear Equations Solvable by First Order Techniques
256(1)
Apollo Reentry
257(1)
Simple Pendulum
258(1)
Asymptotic Behavior of Solutions
259(2)
Introduction to Systems and Phase Plane Analysis
261(77)
Interconnected Fluid Tanks
261(2)
Introduction to the Phase Plane
263(15)
Elimination Method for Systems
278(8)
Coupled Mass-Spring Systems
286(7)
Electrical Circuits
293(8)
Numerical Methods for Higher-Order Equations and Systems
301(14)
Dynamical Systems, Poincare Maps, and Chaos
315(23)
Chapter Summary
325(2)
Review Problems
327(1)
Group Projects for Chapter 5
328(1)
Designing a Landing System for Interplanetary Travel
328(1)
Things That Bob
329(1)
Effects of Hunting on Predator-Prey Systems
330(1)
Periodic Solutions to Volterra-Lotka Systems
331(1)
Hamiltonian Systems
332(2)
Limit Cycles
334(1)
Strange Behavior of Competing Species---Part I
335(1)
Cleaning Up the Great Lakes
336(2)
Theory of Higher-Order Linear Differential Equations
338(31)
Basic Theory of Linear Differential Equations
338(9)
Homogeneous Linear Equations with Constant Coefficients
347(7)
Undetermined Coefficients and the Annihilator Method
354(6)
Method of Variation of Parameters
360(9)
Chapter Summary
364(2)
Review Problems
366(1)
Technical Writing Exercises
366(1)
Group Projects for Chapter 6
367(1)
Justifying the Method of Undetermined Coefficients
367(1)
Transverse Vibrations of Beam
367(2)
Laplace Transforms
369(78)
Introduction: A Mixing Problem
369(4)
Definition of the Laplace Transform
373(9)
Properties of the Laplace Transform
382(6)
Inverse Laplace Transform
388(10)
Solving Initial Value Problems
398(8)
Transforms of Discontinuous and Periodic Functions
406(14)
Convolution
420(9)
Impulses and the Dirac Delta Function
429(7)
Solving Linear Systems with Laplace Transforms
436(11)
Chapter Summary
439(1)
Review Problems
440(1)
Technical Writing Exercises
441(2)
Group Projects for Chapter 7
443(1)
Duhamel's Formulas
443(1)
Frequency Response Modeling
444(2)
Determining System Parameters
446(1)
Series Solutions of Differential Equations
447(80)
Introduction: The Taylor Polynomial Approximation
447(6)
Power Series and Analytic Functions
453(9)
Power Series Solutions to Linear Differential Equations
462(11)
Equations with Analytic Coefficients
473(6)
Cauchy-Euler (Equidimensional) Equations Revisited
479(4)
Method of Frobenius
483(12)
Finding a Second Linearly Independent Solution
495(12)
Special Functions
507(20)
Chapter Summary
520(1)
Review Problems
521(1)
Technical Writing Exercises
522(1)
Group Projects for Chapter 8
523(1)
Spherically Symmetric Solutions to Schrodinger's Equation for the Hydrogen Atom
523(1)
Airy's Equation
524(1)
Buckling of a Tower
524(1)
Aging Spring and Bessel Functions
525(2)
Matrix Methods for Linear Systems
527(73)
Introduction
527(5)
Linear Algebraic Equations
532(4)
Matrices and Vectors
536(12)
Linear Systems in Normal Form
548(9)
Homogeneous Linear Systems with Constant Coefficients
557(12)
Complex Eigenvalues
569(6)
Nonhomogeneous Linear Systems
575(7)
The Matrix Exponential Function
582(18)
Chapter Summary
591(3)
Review Problems
594(1)
Technical Writing Exercises
595(1)
Group Projects for Chapter 9
596(1)
Uncoupling Normal Systems
596(1)
Matrix Laplace Transform Method
596(2)
Undamped Second Order Systems
598(1)
Strange Behavior of Competing Species---Part II
599(1)
Partial Differential Equations
600
Introduction: A Model for Heat Flow
600(3)
Method of Separation of Variables
603(10)
Fourier Series
613(18)
Fourier Cosine and Sine Series
631(5)
The Heat Equation
636(13)
The Wave Equation
649(13)
Laplace's Equation
662
Chapter Summary
675(2)
Technical Writing Exercises
677(1)
Group Projects for Chapter 10
678(1)
Steady-State Temperature Distribution in a Circular Cylinder
678(1)
A Laplace Transform Solution of the Wave Equation
679(1)
Green's Function
680(2)
Numerical Method for Δu = f on a Rectangle
682
APPENDICES A-1(1)
A. Newton's Method
A-1(1)
B. Simpson's Rule
A-3(1)
C. Cramer's Rule
A-5(1)
D. Method of Least Squares
A-6(1)
E. Runge-Kutta Procedure for n Equations
A-9(1)
Answers to Odd-Numbered Problems B-1(1)
Index I-1

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