The Complete Instructor’s Solutions includes all solutions to the exercises found in the text. PowerPoint Lecture Slides and additional instructor’s resources are available. This student supplement contains the answers to every third problem in the textbook, allowing students to assess their progress and review key ideas and concepts discussed throughout the text.

o The new larger trim size and 2-color design make the text a pleasure to read and learn from.

o Numerous NEW engineering and science projects contributed by top mathematicians have been added, and are tied to key mathematical topics in the text.

o Divided into five major parts, the text’s flexibility allows instructors to customize the text to fit their needs. The first eight chapters are ideal for a complete short course in ordinary differential equations.

o The Gram-Schmidt orthogonalization process has been added in Chapter 7 and is used in subsequent chapters.

o All figures now have explanatory captions. Supplements

**Part I: Ordinary Differential Equations**

1. Introduction to Differential Equations

2. First-Order Differential Equations

3. Higher-Order Differential Equations

4. The Laplace Transform

5. Series Solutions of Linear Equations

6. Numerical Solutions of Ordinary Differential Equations

**Part II: Vectors, Matrices, and Vector Calculus**

7. Vectors

8. Matrices

9. Vector Calculus

**Part III: Systems of Differential Equations**

10. Systems of Linear Differential Equations

11. Systems of Nonlinear Differential Equations

**Part IV: Fourier Series and Partial Differential Equations**

12. Orthogonal Functions and Fourier Series

13. Boundary-Value Problems in Rectangular Coordinates

14. Boundary-Value Problems in Other Coordinate Systems

15. Integral Transform Model

16. Numerical Solutions to Partial Differential Equations

**Part V: Complex Analysis**

17. Functions of a Complex Variable

18. Integration in the Complex Plane

19. Series and Residues

20. Conformal Mappings and Applications

**Appendix I **Some Derivative and Integral Formulas

**Appendix II **Gamma Function; Exercises

**Appendix III **Table of Laplace Transforms

**Appendix IV **Conformal Mappings

**Appendix V **Some BASIC Programs for Numerical Methods

**Appendix VI **Selected Answers for Odd-Numbered Problems

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