Barnes & Noble.com - Used Books: A First Course in Differential Equations with Modeling Applications (with C, by Dennis G. Zill, Hardcover

Synopsis

For this eighth edition of a text for a one-semester or one-quarter course in ordinary differential equations, Zill (Loyola Marymount University) adds a CD-ROM of demonstrations and tools for chapter modeling projects, plus section introductions and review material to refresh students on foundations of what the chapter will cover. For this edition, the page size is larger and a two-color design has been incorporated. It is assumed that students have completed at least two semesters of calculus. Annotation ©2004 Book News, Inc., Portland, OR

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An undergraduate text covering first-order and higher-order differential equations, series solutions of linear equations, the Laplace transform, systems of linear first-order differential equations, and numerical solutions of ordinary differential equations. This edition has a clearer delineation to the three major approaches to differential equations: analytical, qualitative, and numerical. It includes new problems that call for the use of a computer algebra system, new conceptual and discussion problems, and new project modules. The author is affiliated with Loyola Marymount University. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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Biography

Dennis G. Zill is professor of mathematics at Loyola Marymount University. His interests are in applied mathematics, special functions, and integral transforms. Dr. Zill received his Ph.D. in applied mathematics and his M.S. from Iowa State University in 1967 and 1964, respectively. He received his B.A. from St. Mary's, Winona, MN, in 1962. Dr. Zill also is former chair of the Mathematics Department at Loyola Marymount University. He is the author or co-author of 13 mathematics texts.

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From the Publisher

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.

Booknews

An undergraduate text covering first-order and higher-order differential equations, series solutions of linear equations, the Laplace transform, systems of linear first-order differential equations, and numerical solutions of ordinary differential equations. This edition has a clearer delineation to the three major approaches to differential equations: analytical, qualitative, and numerical. It includes new problems that call for the use of a computer algebra system, new conceptual and discussion problems, and new project modules. The author is affiliated with Loyola Marymount University. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Details from Seller

ISBN: 0534418783
Publisher: Cengage Learning
Pub. Date: October 2004
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Comments from the Seller: 2004 Hardcover New Brand New! ! ! ! ! ! What a Deal! ! ! ! ! !

Table of Contents

	Preface	ix
	Acknowledgments	xv
1	Introduction to Differential Equations	1
1.1	Definitions and Terminology	2
1.2	Initial-Value Problems	15
1.3	Differential Equations as Mathematical Models	22
	Chapter 1 in Review	37
2	First-Order Differential Equations	39
2.1	Solution Curves Without the Solution	40
2.2	Separable Variables	51
2.3	Linear Equations	60
2.4	Exact Equations	72
2.5	Solutions by Substitutions	80
2.6	A Numerical Solution	86
	Chapter 2 in Review	92
3	Modeling with First-Order Differential Equations	95
3.1	Linear Equations	96
3.2	Nonlinear Equations	109
3.3	Systems of Linear and Nonlinear Differential Equations	121
	Chapter 3 in Review	130
	Project Module: Harvesting of Renewable Natural Resources	133
4	Higher-Order Differential Equations	138
4.1	Preliminary Theory: Linear Equations	139
4.1.1	Initial-Value and Boundary-Value Problems	139
4.1.2	Homogeneous Equations	142
4.1.3	Nonhomogeneous Equations	148
4.2	Reduction of Order	154
4.3	Homogeneous Linear Equations with Constant Coefficients	158
4.4	Undetermined Coefficients--Superposition Approach	167
4.5	Undetermined Coefficients--Annihilator Approach	178
4.6	Variation of Parameters	188
4.7	Cauchy-Euler Equation	193
4.8	Solving Systems of Linear Equations by Elimination	201
4.9	Nonlinear Equations	207
	Chapter 4 in Review	212
5	Modeling with Higher-Order Differential Equations	215
5.1	Linear Equations: Initial-Value Problems	216
5.1.1	Spring/Mass Systems: Free Undamped Motion	216
5.1.2	Spring/Mass Systems: Free Damped Motion	220
5.1.3	Spring/Mass Systems: Driven Motion	224
5.1.4	Series Circuit Analogue	227
5.2	Linear Equations: Boundary-Value Problems	237
5.3	Nonlinear Equations	247
	Chapter 5 in Review	259
	Project Module: The Collapse of the Tacoma Narrows Suspension Bridge	263
6	Series Solutions of Linear Equations	267
6.1	Solutions About Ordinary Points	268
6.1.1	Review of Power Series	268
6.1.2	Power Series Solutions	271
6.2	Solutions About Singular Points	280
6.3	Two Special Equations	292
	Chapter 6 in Review	304
7	The Laplace Transform	306
7.1	Definition of the Laplace Transform	307
7.2	Inverse Transform and Transforms of Derivatives	314
7.3	Translation Theorems	324
7.3.1	Translation on the s-Axis	324
7.3.2	Translation on the t-Axis	328
7.4	Additional Operational Properties	338
7.5	Dirac Delta Function	351
7.6	Systems of Linear Equations	354
	Chapter 7 in Review	361
8	Systems of Linear First-Order Differential Equations	364
8.1	Preliminary Theory	365
8.2	Homogeneous Linear Systems with Constant Coefficients	375
8.2.1	Distinct Real Eigenvalues	376
8.2.2	Repeated Eigenvalues	380
8.2.3	Complex Eigenvalues	384
8.3	Variation of Parameters	393
8.4	Matrix Exponential	399
	Chapter 8 in Review	404
	Project Module: Earthquake Shaking of Multistory Buildings	406
9	Numerical Solutions of Ordinary Differential Equations	410
9.1	Euler Methods and Error Analysis	411
9.2	Runge-Kutta Methods	417
9.3	Multistep Methods	424
9.4	Higher-Order Equations and Systems	427
9.5	Second-Order Boundary-Value Problems	433
	Chapter 9 in Review	438
	Appendixes	1
I	Gamma Functions	1
II	Introduction to Matrices	3
III	Laplace Transforms	25
	Selected Answers for Odd-Numbered Problems	1
	Index	1

A First Course in Differential Equations with Modeling Applications (with C by Dennis G. Zill

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