Differential Equations with Boundary-Value Problems

by Dennis G. Zill

Overview

Straightforward and easy to read, Zill's DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 10th EDITION, gives you a thorough overview of the topics typically taught in a differential equations first course as well as an introduction to boundary-value problems and partial differential equations. Your study will be supported by a bounty of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions and more.

Product Details

ISBN-13:	9780357760451
Publisher:	Cengage Learning
Publication date:	06/12/2023
Edition description:	10th ed.
Pages:	640
Product dimensions:	8.40(w) x 10.50(h) x 1.20(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

PREFACE. ACKNOWLEDGEMENTS. 1. INTRODUCTION TO DIFFERENTIAL EQUATIONS. Definition and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Review. 2. FIRST-ORDER DIFFERENTIAL EQUATIONS. Solutions Curves Without the Solution. Separable Variables. Linear Equations. Exact Equations. Solutions by Substitutions. A Numerical Solution. Review. 3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS. Linear Equations. Nonlinear Equations. Systems of Linear and Nonlinear Differential Equations. Review. Project Module: Harvesting of Renewable Natural Resources, by Gilbert N. Lewis. 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 Equations by Elimination. Nonlinear Equations. Review. 5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear Equations: Initial-Value Problems. Linear Equations: Boundary-Value Problems. Nonlinear Equations. Review. Project Module: The Collapse of the Tacoma Narrows Suspension Bridge, by Gilbert N. Lewis. 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Solutions About Ordinary Points. Solutions About Singular Points. Two Special Equations. Review. 7. THE LAPLACE TRANSFORM. Definition of the Laplace Transform. Inverse Transform and Transforms of a Derivatives. Translation Theorems. Additional Operational Properties. Dirac Delta Function. Systems of Linear Equations. Review. 8. SYSTEMS OF LINEAR FIRST-ORDER DIFFERNTIAL EQUATIONS. Preliminary Theory.Homogeneous Linear Systems with Constant Coefficients. Variation of Parameters. Matrix Exponential. Review. Project Module: Earthquake Shaking of Multistory Buildings, by Gilbert N. Lewis. 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. Review. 10. PLANE AUTONOMOUS SYSTEMS AND STABILITY. Autonomous Systems, Critical Points, and Periodic Solutions. Stability of Linear Systems. Linearization and Local Stability. Modeling Using Autonomous Systems. Review. 11. ORTHOGONAL FUNCTIONS AND FOURIER SERIES. Orthogonal Functions. Fourier Series. Fourier Cosine and Sine Series. Sturm-Liouville Problem. Bessel and Legendre Series. Review. 12. PARTIAL DIFFERENTIAL EQUATIONS AND BOUNDARY-VALUE PROBLEMS IN RECTANGULAR COORDINATES. Separable Partial Differential Equations. Classical Equations and Boundary-Value Problems. Heat Equation. Wave Equation. Laplace's Equation. Nonhomogeneous Equations and Boundary Conditions. Orthogonal Series Expansions. Boundary-Value Problems Involving Fourier Series in Two Variables. Review. 13. BOUNDARY-VALUE PROBLEMS IN OTHER COORDINATE SYSTEMS. Problems Involving Laplace's Equation in Polar Coordinates. Problems in Polar and Cylindrical Coordinates: Bessel Functions. Problems in Spherical Coordinates: Legendre Polynomials. Review. 14. INTEGRAL TRANSFORM METHOD. Error Function. Applications of the Laplace Transform. Fourier Integral. Fourier Transforms. Review. 15. NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS. Elliptic Equations. Parabolic Equations. Hyperbolic Equations. Review. APPENDIX I: GAMMA FUNCTION. APPENDIX II: INTRODUCTION TO MATRICES. APPENDIX III: LAPLACE TRANSFORMS. SELECTED ANSWERS TO ODD-NUMBERED PROBLEMS. INDEX.

Editorial Reviews

New edition of an undergraduate text written with the student's understanding in mind, that is, the author has aimed for clear, straightforward readability, and theory is kept to a "first course" level. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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