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Edition: 4TH 95

Copyright: 1995

Publisher: PWS-Kent Publishing Co.

Published: 1995

International: No

Copyright: 1995

Publisher: PWS-Kent Publishing Co.

Published: 1995

International: No

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The computer plays a prominent role throughout the text in generating computer graphics used to display such concepts as direction fields, phase portraits, surfaces and vector fields, convergence of Fourier series, the Gibbs phenomenon, and filtering noise from signals. The author took care to make his presentation of material interesting and the text's format useful and easily read. This edition was reorganized in part to provide a more logical structure and to more fully develop the connections among topics. All of the problem sets and solutions were extensively class tested and checked for accuracy, level of difficulty and suitability. Among the case studies included are an FFT analysis of tidal data and a problem in radioactive waste disposal.

- Case studies explore how mathematical models are used to analyze some interesting phenomena.
- Fast Fourier transform has been expanded to two sections, and includes applications.
- Direction Fields are introduced in Chapter 1, allowing a visual representation of the solution to differential equations and making the subsequent analytic solution more meaningful.
- Computer Graphics are used to display such concepts as direction fields, phase portraits, and Gibb's phenomenon, to name a few.
- "A Guide to Major Results" is provided as an aid to locating important results.
- This edition was reorganized and condensed for easier use with technology; it presents a wider range of applications; and includes a redrawn art program with computer graphics.

**O'Neil, Peter V. : University of Alabama**

**PART 1: ORDINARY DIFFERENTIAL EQUATIONS. **

1. First Order Differential Equations.

2. Second Order Differential Equations.

3. The Laplace Transform.

4. Series Solutions.

5. Numerical Approximation Of Solutions.

6. Sturm-Liouville Theory, Eigenfunction Expansions And Special Functions.

**PART 2: VECTORS AND LINEAR ALGEBRA. **

7. Vectors And Vector Spaces.

8. Matrices, Determinants, And Systems Of Linear Equations.

9. Eigenvalues And Diagonalization.

**PART 3: SYSTEMS OF DIFFERENTIAL EQUATIONS AND QUALITATIVE METHODS. **

10. Linear Systems Of Differential Equations.

11. Nonlinear Differential Equations And Qualitative Methods.

**PART 4: VECTOR ANALYSIS. **

12. Vector Differential Calculus.

13. Vector Integral Calculus.

**PART 5: FOURIER ANALYSIS AND BOUNDARY VALUE PROBLEMS. **

14. Fourier Series And Integrals.

15. Fourier Transforms.

16. Partial Differential Equations And Boundary Value Problems.

**PART 6: COMPLEX ANALYSIS. **

17. Complex Numbers And Complex Functions.

18. Complex Integration.

19. Conformal Mappings And Some Applications.

**PART 7: HISTORICAL NOTES. **

** **Notation.

Guide to Major Results.

Answers and Solutions to Selected Odd-Numbered Problems.

Index.

Summary

The computer plays a prominent role throughout the text in generating computer graphics used to display such concepts as direction fields, phase portraits, surfaces and vector fields, convergence of Fourier series, the Gibbs phenomenon, and filtering noise from signals. The author took care to make his presentation of material interesting and the text's format useful and easily read. This edition was reorganized in part to provide a more logical structure and to more fully develop the connections among topics. All of the problem sets and solutions were extensively class tested and checked for accuracy, level of difficulty and suitability. Among the case studies included are an FFT analysis of tidal data and a problem in radioactive waste disposal.

- Case studies explore how mathematical models are used to analyze some interesting phenomena.
- Fast Fourier transform has been expanded to two sections, and includes applications.
- Direction Fields are introduced in Chapter 1, allowing a visual representation of the solution to differential equations and making the subsequent analytic solution more meaningful.
- Computer Graphics are used to display such concepts as direction fields, phase portraits, and Gibb's phenomenon, to name a few.
- "A Guide to Major Results" is provided as an aid to locating important results.
- This edition was reorganized and condensed for easier use with technology; it presents a wider range of applications; and includes a redrawn art program with computer graphics.

Author Bio

**O'Neil, Peter V. : University of Alabama**

Table of Contents

**PART 1: ORDINARY DIFFERENTIAL EQUATIONS. **

1. First Order Differential Equations.

2. Second Order Differential Equations.

3. The Laplace Transform.

4. Series Solutions.

5. Numerical Approximation Of Solutions.

6. Sturm-Liouville Theory, Eigenfunction Expansions And Special Functions.

**PART 2: VECTORS AND LINEAR ALGEBRA. **

7. Vectors And Vector Spaces.

8. Matrices, Determinants, And Systems Of Linear Equations.

9. Eigenvalues And Diagonalization.

**PART 3: SYSTEMS OF DIFFERENTIAL EQUATIONS AND QUALITATIVE METHODS. **

10. Linear Systems Of Differential Equations.

11. Nonlinear Differential Equations And Qualitative Methods.

**PART 4: VECTOR ANALYSIS. **

12. Vector Differential Calculus.

13. Vector Integral Calculus.

**PART 5: FOURIER ANALYSIS AND BOUNDARY VALUE PROBLEMS. **

14. Fourier Series And Integrals.

15. Fourier Transforms.

16. Partial Differential Equations And Boundary Value Problems.

**PART 6: COMPLEX ANALYSIS. **

17. Complex Numbers And Complex Functions.

18. Complex Integration.

19. Conformal Mappings And Some Applications.

**PART 7: HISTORICAL NOTES. **

** **Notation.

Guide to Major Results.

Answers and Solutions to Selected Odd-Numbered Problems.

Index.

Publisher Info

Publisher: PWS-Kent Publishing Co.

Published: 1995

International: No

Published: 1995

International: No

The computer plays a prominent role throughout the text in generating computer graphics used to display such concepts as direction fields, phase portraits, surfaces and vector fields, convergence of Fourier series, the Gibbs phenomenon, and filtering noise from signals. The author took care to make his presentation of material interesting and the text's format useful and easily read. This edition was reorganized in part to provide a more logical structure and to more fully develop the connections among topics. All of the problem sets and solutions were extensively class tested and checked for accuracy, level of difficulty and suitability. Among the case studies included are an FFT analysis of tidal data and a problem in radioactive waste disposal.

- Case studies explore how mathematical models are used to analyze some interesting phenomena.
- Fast Fourier transform has been expanded to two sections, and includes applications.
- Direction Fields are introduced in Chapter 1, allowing a visual representation of the solution to differential equations and making the subsequent analytic solution more meaningful.
- Computer Graphics are used to display such concepts as direction fields, phase portraits, and Gibb's phenomenon, to name a few.
- "A Guide to Major Results" is provided as an aid to locating important results.
- This edition was reorganized and condensed for easier use with technology; it presents a wider range of applications; and includes a redrawn art program with computer graphics.

**O'Neil, Peter V. : University of Alabama**

**PART 1: ORDINARY DIFFERENTIAL EQUATIONS. **

1. First Order Differential Equations.

2. Second Order Differential Equations.

3. The Laplace Transform.

4. Series Solutions.

5. Numerical Approximation Of Solutions.

6. Sturm-Liouville Theory, Eigenfunction Expansions And Special Functions.

**PART 2: VECTORS AND LINEAR ALGEBRA. **

7. Vectors And Vector Spaces.

8. Matrices, Determinants, And Systems Of Linear Equations.

9. Eigenvalues And Diagonalization.

**PART 3: SYSTEMS OF DIFFERENTIAL EQUATIONS AND QUALITATIVE METHODS. **

10. Linear Systems Of Differential Equations.

11. Nonlinear Differential Equations And Qualitative Methods.

**PART 4: VECTOR ANALYSIS. **

12. Vector Differential Calculus.

13. Vector Integral Calculus.

**PART 5: FOURIER ANALYSIS AND BOUNDARY VALUE PROBLEMS. **

14. Fourier Series And Integrals.

15. Fourier Transforms.

16. Partial Differential Equations And Boundary Value Problems.

**PART 6: COMPLEX ANALYSIS. **

17. Complex Numbers And Complex Functions.

18. Complex Integration.

19. Conformal Mappings And Some Applications.

**PART 7: HISTORICAL NOTES. **

** **Notation.

Guide to Major Results.

Answers and Solutions to Selected Odd-Numbered Problems.

Index.