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First Course in Differential Equations With Modeling Applications - With CD (8TH 05 - Old Edition)by Dennis G. Zill
Synopses & ReviewsPlease note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.
Now enhanced with the innovative DE Tools CD-ROM and the iLrn teaching and learning system, this proven text explains the "how" behind the material and strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This accessible text speaks to students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Author Dennis G. Zill wrote this book with the student's understanding kept firmly in mind. He presents the material in a straightforward, readable, and helpful manner, while keeping the level of theory consistent with the notion of a "first course."
Book News Annotation:
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 (booknews.com)
A First Course in Differential Equations with Modeling Applications, 9th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.
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.
About the Author
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 in Winona, Minnesota, 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.
Table of Contents
1. INTRODUCTION TO DIFFERENTIAL EQUATIONS. Definitions and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Chapter 1 in Review. Project 1: Diving Deception Pass. 2. FIRST-ORDER DIFFERENTIAL EQUATIONS. Solution Curves Without a Solution. Separable Variables. Linear Equations. Exact Equations. Solutions by Substitutions. A Numerical Method. Chapter 2 in Review. Project 2: Harvesting Natural Resources. 3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS. Linear Models. Nonlinear Models. Modeling with Systems of Differential Equations. Chapter 3 in Review. Project 3: Swimming the Salmon River. 4. HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear Differential Equations: Basic Theory. Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients- Superposition Approach. Undetermined Coefficients- Annihilator Approach. Variation of Parameters. Cauchy-Euler Equation. Solving Systems of Linear Equations by Elimination. Nonlinear Differential Equations. Chapter 4 in Review. Project 4: Bungee Jumping. 5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear Models: Initial-Value Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. Chapter 5 in Review. Project 5: The Collapse of Galloping Gertie. 6: SERIES SOLUTIONS OF LINEAR EQUATIONS. Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review. Project 6: Defeating Tamarisk. 7. LAPLACE TRANSFORM. Definition of the Laplace Transform. Inverse Transform and Transforms of Derivatives. Operational Properties I. Operational Properties II. Dirac Delta Function. Systems of Linear Differential Equations. Chapter 7 in Review. Project 7: Murder at the Mayfair. 8. SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. Preliminary Theory. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review. Project 8: Designing for Earthquakes. 9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS. Euler Methods and Error Analysis. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review. Project 9: The Hammer. Appendix I: Gamma Function. Appendix II: Introduction to Matrices. Appendix III: Laplace Transforms. Selected Answers for Odd-Numbered Problems.
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