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by Dennis G. Zill and Michael R. Cullen

Edition: 6TH 05Copyright: 2005

Publisher: Brooks/Cole Publishing Co.

Published: 2005

International: No

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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.

**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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Summary

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.

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.

Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 2005

International: No

Published: 2005

International: No

**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.