A First Course in Differential Equations with Modeling Applications

by Dennis G. Zill

Overview

Straightforward and easy to read, A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 11th Edition, gives you a thorough overview of the topics typically taught in a first course in differential equations. Your study of differential equations and its applications will be supported by a bounty of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and MindTap Math - an available option which includes an online version of the book, lecture videos, a pre-course assessment, and more.

Product Details

ISBN-13:	9781305965720
Publisher:	Cengage Learning
Publication date:	01/01/2017
Series:	MindTap Course List
Edition description:	New Edition
Pages:	480
Product dimensions:	8.40(w) x 10.80(h) x 0.90(d)

About the Author

Dennis Zill, Ph.D., received a doctorate in applied mathematics from Iowa State University and is a former professor of mathematics at Loyola Marymount University in Los Angeles, Loras College in Iowa and California Polytechnic State University. He is also the former chair of the mathematics department at Loyola Marymount University, where he currently holds the title of Professor Emeritus of Mathematics. Zill has interests in astronomy, modern literature, music, golf and good wine, while his research interests include special functions, differential equations, integral transformations and complex analysis.

Table of Contents

1. INTRODUCTION TO DIFFERENTIAL EQUATIONS. Definitions and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Chapter 1 in Review. 2. FIRST-ORDER DIFFERENTIAL EQUATIONS. Solution Curves Without a Solution. Separable Variables. Linear Equations. Exact Equations and Integrating Factors. Solutions by Substitutions. A Numerical Method. Chapter 2 in Review. 3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS. Linear Models. Nonlinear Models. Modeling with Systems of First-Order Differential Equations. Chapter 3 in Review. 4. HIGHER-ORDER DIFFERENTIAL EQUATIONS. Preliminary Theory-Linear Equations. 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 Differential Equations by Elimination. Nonlinear Differential Equations. Chapter 4 in Review. 5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear Models: Initial-Value Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. Chapter 5 in Review. 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Review of Power Series Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review. 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. 8. SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. Preliminary Theory. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review. 9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS. Euler Methods. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review. Appendix I. Gamma Function. Appendix II. Matrices. Appendix III. Laplace Transforms. Answers for Selected Odd-Numbered Problems.

Editorial Reviews

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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