Differential Equations

Differential Equations
Frank Ayres

including 560 solved problems
1. Origin of Differential Equations
2. Solutions of Differential Equations
3. Equations of First Order and First Degree
4. Equations of First Order and First Degree - Variables Separable and Reduction to Variables Separable
5. Equations of First Order and First Degree - Exact Equations and Reduction to Exact Equations
6. Equations of First Order and First Degree - Linear Equations and Those Reducible to That Form
7. Geometric Applications
8. Physical Applications
9. Equations of First Order and Higher Degree
10. Singular Solutions - Extraneous Loci
11. Applications of First Order and Higher Degree Equations
12. Linear Equations of Order n
13. Homogeneous Linear Equations with Constant Coefficients
14. Linear Equations with Constant Coefficients
15. Linear Equations with Constant Coefficients - Variation of Parameters, Undetermined Coefficients
16. Linear Equations with Constant Coefficients - Short Methods
17. Linear Equations with Constant Coefficients - The Cauchy and Legendre Linear Equations
18. Linear Equations with Variable Coefficients - Equations of the Second Order
19. Linear Equations with Variable Coefficients - Miscellaneous Types
20. Applications of Linear Equations
21. Systems of Simultaneous Equations
22. Total Differential Equations
23. Application of Total and Simultaneous Equations
24. Numerical Approximations to Solutions
25. Integration in Series
26. Integration in Series
27. The Legendre, Bessel and Gauss Equations
28. Partial Differential Equations
29. Linear Partial Differential Equations of Order One
30. Non-Linear Partial Differential Equations of Order One
31. Homogeneous Partial Differential Equations of Higher Order with Constant Coefficients
32. Non-Homogeneous Partial Differential Equations with Constant Coefficients
33. Partial Differential Equations of Order Two with Variable Coefficients