Solving equations with physical understanding J.R. Acton & P.T. Squire

Mathematical preliminaries
Estimation of time constants by exponential trial functions
Estimation of length constants by exponential trial functions
Parabolic trial functions
The QSTF method for unforced oscillations
Forced oscillation and resonance
Exact solution of partial differential equations
Estimation of lowest eigenvalues by parabolic trial functions
The QSTF method for conduction and diffusion equations
Extending the QSTF method

In creating mathematical models of real processes, scientists, engineers and students frequently encounter differential equations whose exact solutions are necessarily complicated and are normally solvable only by computer or through complex formal mathematics. This practical book demonstrates how approximate methods may be used to minimize these mathematical difficulties, giving the reader physical understanding both of the solution process and the final result. Intended for undergraduates and graduate students, teachers of physics, engineering and other applied sciences, professional and applied scientists and engineers.