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Cover type: Hardback

Edition: 8TH 13

Copyright: 2013

Publisher: Brooks/Cole Publishing Co.

Published: 2013

International: No

Edition: 8TH 13

Copyright: 2013

Publisher: Brooks/Cole Publishing Co.

Published: 2013

International: No

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DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 8th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible book speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, ''Remarks'' boxes, definitions, and group projects. Written in a straightforward, readable, and helpful style, the book provides a thorough treatment of boundary-value problems and partial 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.

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 and Orthogonal Functions. 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. 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: Matrices.

Appendix III: Laplace Transforms.

Answers for Selected Odd-Numbered Problems.

- Windows 7/8, or Mac OS X 10.6 or above

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Summary

DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 8th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible book speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, ''Remarks'' boxes, definitions, and group projects. Written in a straightforward, readable, and helpful style, the 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.

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.

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 and Orthogonal Functions. 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. 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: Matrices.

Appendix III: Laplace Transforms.

Answers for Selected Odd-Numbered Problems.

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.

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 and Orthogonal Functions. 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. 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: Matrices.

Appendix III: Laplace Transforms.

Answers for Selected Odd-Numbered Problems.

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Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 2013

International: No

Published: 2013

International: No

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.

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 and Orthogonal Functions. 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. 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: Matrices.

Appendix III: Laplace Transforms.

Answers for Selected Odd-Numbered Problems.

- Windows 7/8, or Mac OS X 10.6 or above

eTextbooks and eChapters can be viewed by using the free reader listed below.

Be sure to check the format of the eTextbook/eChapter you purchase to know which reader you will need. After purchasing your eTextbook or eChapter, you will be emailed instructions on where and how to download your free reader.

Due to the size of eTextbooks, a high-speed Internet connection (cable modem, DSL, LAN) is required for download stability and speed. Your connection can be wired or wireless.

Being online is not required for reading an eTextbook after successfully downloading it. You must only be connected to the Internet during the download process.

Click Here to access the VitalSource Bookshelf FAQ

VitalSource

**Copying:** Allowed, 10 selections may be copied every 180 days

**Printing:** Allowed, 10 prints for 180 days

**Expires:** Yes, may be used for 180 days after activation

**Reading Aloud:** Allowed

**Sharing:** Not Allowed

**Min. Software Version:** Online: No additional software required

Offline: VitalSource Bookshelf

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**Copying** - Books that cannot be copied will show "Not Allowed." Otherwise, this will detail the number of times it can be copied, or "Allowed with no limits."

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