Differential Equations with Boundary-Value Problems, 6th Edition / Edition 6

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Overview

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. This book was written with the student's understanding firmly in mind. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.

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Editorial Reviews

From the Publisher
"Zill and Cullen is exceptionally well laid-out, making it easy for students to follow, with good examples, summaries, and straightforward exposition. Definitions, theorems, proofs, etc, are also clearly stated. Important results are nicely highlighted. Excellent review exercises are provided, with fill-in the blank and t/f type questions, as well as problems." "The exercises are a strength, with graded level of difficulty, with a few challenging problems for more capable students. Skill and concepts are well balanced in the exercises, and there are sufficient numbers of each; there are appropriate applications, both classic and modern. There are new problems employing CAS as well as lab exercise. These are a real plus."

"I consider Zill's book to be extremely well written overall with an excellent and wide ranging selection of problems." "Overall, I am impressed with the quality of the writing, the examples and the exercises in both the early and the late chapters and find it appropriate for both weak and strong students."

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Product Details

  • ISBN-13: 9780534418878
  • Publisher: Cengage Learning
  • Publication date: 10/15/2004
  • Edition description: With CD-ROM and iLrn
  • Edition number: 6
  • Pages: 640
  • Product dimensions: 8.60 (w) x 11.00 (h) x 1.10 (d)

Meet 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.

Professor Michael Cullen, late of Loyola Marymount University, was awarded the President's Fritz B. Burns Distinguished Teaching Award for Excellence in Teaching and Scholarship in 1999. Dr. Cullen received his Ph.D. in complex variables from the University of Iowa in 1968. He received his M.S. from the University of Iowa in 1967 and his B.S. from Loyola University of Los Angeles in 1965. His interest was in biomathematics. Dr. Cullen also authored two texts in mathematics: MATHEMATICS FOR THE BIOSCIENCES and LINEAR MODELS IN BIOLOGY.

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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. 10. PLANE AUTONOMOUS SYSTEMS. Autonomous Systems. Stability of Linear Systems. Linearization and Local Stability. Autonomous Systems as Mathematical Models. Chapter 10 in Review. 11. ORTHOGONAL FUNCTIONS AND FOURIER SERIES. Orthogonal Functions. Fourier Series. Fourier Cosine and Sine Series. Sturm-Liouville Problem. Bessel and Legendre Series. Chapter 11 in Review. 12. BOUNDARY-VALUE PROBLEMS IN RECTANGULAR COORDINATES. Separable Partial Differential Equations. Classical PDE's and Boundary-Value Problems. Heat Equation. Wave Equation. Laplace's Equation. Nonhomogeneous Boundary-Value Problems. Orthogonal Series Expansions. Higher-Dimensional Problems. Chapter 12 in Review. 13. BOUNDARY-VALUE PROBLEMS IN OTHER COORDINATE SYSTEMS. Polar Coordinates. Polar and Cylindrical Coordinates. Spherical Coordinates. Chapter 13 in Review. 14. INTEGRAL TRANSFORM METHOD. Error Function. Applications of the Laplace Transform. Fourier Integral. Fourier Transforms. Chapter 14 in Review. 15. NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS. Laplace's Equation. Heat Equation. Wave Equation. Chapter 15 in Review. Appendix I: Gamma Function. Appendix II: Introduction to Matrices. Appendix III: Laplace Transforms. Selected Answers for Odd-Numbered Problems.

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