Elementary differential equations / Earl D Rainville; Phillip Edward Bedient; Richard E Bedient

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