Elementary Differential Equations

<br> <br> &nbsp;1. Definitions; Families of Curves. <br> <br> <br> &nbsp;2. Equations of Order One. <br> <br> <br> &nbsp;3. Numerical Methods. <br> <br> <br> &nbsp;4. Elementary Applications. <br> <br> <br> &nbsp;5. Additional Topics on Equations of Order One. <br> <br> <br> &nbsp;6. Linear Differential Equations. <br> <br> <br> &nbsp;7. Linear Equations with Constant Coefficients. <br> <br> <br> &nbsp;8. Nonhomogeneous Equations: Undetermined Coefficients. <br> <br> <br> &nbsp;9. Variation of Parameters. <br> <br> <br> 10. Applications. <br> <br> <br> 11. Linear Systems of Equations. <br> <br> <br> 12. Nonhomogeneous Systems of Equations. <br> <br> <br> 13. The Existence and Uniqueness of Solutions. <br> <br> <br> 14. The Laplace Transform. <br> <br> <br> 15. Inverse Transforms. <br> <br> <br> 16. Nonlinear Equations. <br> <br> <br> 17. Power Series Solutions. <br> <br> <br> 18. Solutions Near Regular Singular Points. <br> <br> <br> 19. Equations of Hypergeometric Type. <br> <br> <br> 20. Partial Differential Equations. <br> <br> <br> 21. Orthogonal Sets of Functions. <br> <br> <br> 22. Fourier Series. <br> <br> <br> 23. Boundary Value Problems. <br> <br> <br> 24. Additional Properties of the Laplace Transform. <br> <br> <br> 25. Partial Differential Equations Transform Methods. <br> <br> <br> Answers to Odd-numbered Exercises. <br> <br> <br> Index. <br>