Table of Contents:

• 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

• Index