ABSTRACT
This chapter constructs asymptotic expansions for the solutions of linear differential equations. It analyzes the behavior of solutions for large values of the independent variable using the method of dominant balance. In Murray's text a systematic approach is described for the application of the method of dominant balance. The method of dominant balance provides valuable information about the behavior of solutions for large values of the independent variable. The chapter also analyzes the behavior for large values of parameter using the WKB method. The WKB method provides a powerful approximation technique for determining large eigen values of boundary value problems. Eigen value problems arise in fields of science. They occur in the description of wave motion in classical physics where, for example, the possible wavelengths of sound in pipes or of vibrating strings are determined by solving an eigen value problem. An example of occurrence of eigen values in modern physics is as the energy levels in Schrodinger's wave equation.
