by Dennis G. Zill and Michael R. Cullen
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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.
Dennis G. Zill and Michael R. Cullen
ISBN13: 978-0534418878Now 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.