A First Course in Differential Equations With Modeling Applications

by Zill, Dennis G.

• ISBN13: 9780534379995
• ISBN10: 0534379990
• Format: Hardcover
• Copyright: 2000-10-05
• Publisher: Brooks Cole

Summary

Master differential equations and succeed in your course with A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS with accompanying CD-ROM and technology! Straightfoward and readable, this mathematics text provides you with tools such as examples, explanations, definitions, and applications designed to help you succeed. The accompanying DE Tools CD-ROM makes helps you master difficult concepts through twenty-one demonstration tools such as Project Tools and Text Tools. Studying is made easy with iLrn Tutorial, a text-specific, interactive tutorial software program that gives the practice you need to succeed.

Table of Contents

Preface	ix
Acknowledgments	xv
Introduction To Differential Equations	1	(38)
Definitions and Terminology	2	(13)
Initial-Value Problems	15	(7)
Differential Equations as Mathematical Models	22	(17)
Chapter 1 in Review	37	(2)
First-Order Differential Equations	39	(56)
Solution Curves Without the Solution	40	(11)
Separable Variables	51	(9)
Linear Equations	60	(12)
Exact Equations	72	(8)
Solutions by Substitutions	80	(6)
A Numerical Solution	86	(9)
Chapter 2 in Review	92	(3)
Modeling With First-Order Differential Equations	95	(43)
Linear Equations	96	(13)
Nonlinear Equations	109	(12)
Systems of Linear and Nonlinear Differential Equations	121	(17)
Chapter 3 in Review	130	(3)
Project Module: Harvesting of Renewable Natural Resources	133	(5)
Gilbert N. Lewis
Higher-Order Differential Equations	138	(77)
Preliminary Theory: Linear Equations	139	(15)
Initial-Value and Boundary-Value Problems	139	(3)
Homogeneous Equations	142	(6)
Nonhomogeneous Equations	148	(6)
Reduction of Order	154	(4)
Homogeneous Linear Equations with Constant Coefficients	158	(9)
Undetermined Coefficients--Superposition Approach	167	(11)
Undetermined Coefficients--Annihilator Approach	178	(10)
Variation of Parameters	188	(5)
Cauchy-Euler Equation	193	(8)
Solving Systems of Linear Equations by Elimination	201	(6)
Nonlinear Equations	207	(8)
Chapter 4 in Review	212	(3)
Modeling with Higher-Order Differential Equations	215	(52)
Linear Equations: Initial-Value Problems	216	(21)
Spring/Mass Systems: Free Undamped Motion	216	(4)
Spring/Mass Systems: Free Damped Motion	220	(4)
Spring/Mass Systems: Driven Motion	224	(3)
Series Circuit Analogue	227	(10)
Linear Equations: Boundary-Value Problems	237	(10)
Nonlinear Equations	247	(20)
Chapter 5 in Review	259	(4)
Project Module: The Collapse of the Tacoma Narrows Suspension Bridge	263	(4)
Gilbert N. Lewis
Series Solutions of Linear Equations	267	(39)
Solutions About Ordinary Points	268	(12)
Review of Power Series	268	(3)
Power Series Solutions	271	(9)
Solutions About Singular Points	280	(12)
Two Special Equations	292	(14)
Chapter 6 in Review	304	(2)
The Laplace Transform	306	(58)
Definition of the Laplace Transform	307	(7)
Inverse Transform and Transforms of Derivatives	314	(10)
Translation Theorems	324	(14)
Translation on the s-Axis	324	(4)
Translation on the t-Axis	328	(10)
Additional Operational Properties	338	(13)
Dirac Delta Function	351	(3)
Systems of Linear Equations	354	(10)
Chapter 7 in Review	361	(3)
Systems of Linear First-Order Differential Equations	364	(46)
Preliminary Theory	365	(10)
Homogeneous Linear Systems with Constant Coefficients	375	(18)
Distinct Real Eigenvalues	376	(4)
Repeated Eigenvalues	380	(4)
Complex Eigenvalues	384	(9)
Variation of Parameters	393	(6)
Matrix Exponential	399	(11)
Chapter 8 in Review	404	(2)
Project Module: Earthquake Shaking of Multistory Buildings	406	(4)
Gilbert N. Lewis
Numerical Solutions of Ordinary Differential Equations	410
Euler Methods and Error Analysis	411	(6)
Runge-Kutta Methods	417	(7)
Multistep Methods	424	(3)
Higher-Order Equations and Systems	427	(6)
Second-Order Boundary-Value Problems	433
Chapter 9 in Review	438
APPENDIXES	1	(1)
I Gamma Functions	1	(2)
II Introduction to Matrices	3	(22)
III Laplace Transforms	25
Selected Answers for Odd-Numbered Problems	1	(1)
Index	1