Simmons G.F. Differential Equations with Applications and Historical Notes

2nd Edition. — McGraw-Hill, 1991. — 629 p. — ISBN: 0070575401A revision of a much-admired text distinguished by the exceptional prose and historical/mathematical context that have made Simmons' books classics. The Second Edition includes expanded coverage of Laplace transforms and partial differential equations as well as a new chapter on numerical methods.The Nature of Differential Equations.
First Order Equations.
Second Order Linear Equations.
Qualitative Properties of Solutions.
Power Series Solutions and Special Functions.
Fourier Series and Orthogonal Functions.
Partial Differential Equations and Boundary Value Problems.
Some Special Functions of Mathematical Physics.
Laplace Transforms.
Systems of First Order Equations.
Nonlinear Equations.
The Calculus of Variations.
The Existence and Uniqueness of Solutions.
Numerical Methods.