The techniques that can be used to solve nonlinear problems are very different from those that are used to solve linear problems. Most courses in analysis and applied mathematics attack linear problems simply because they are easier to solve. The information that is needed to solve them is not as involved or technical in nature as that which is usually required to solve a corresponding nonlinear problem. This applies not only to the practical material but also to the theoretical background.

As an example, it is usually sufficient in dealing with linear problems in analysis to apply Riemann integration to functions that are piecewise continuous. Rarely is more needed. In considering the convergence of series, uniform convergence usually suffices. In general, concepts from functional analysis are not needed; linear algebra is usually sufficient. A student can go quite far in the study of linear problems without being exposed to Lebesgue integration or functional analysis.

However, there are many nonlinear problems that arise in applied mathematics and sciences that require much more theoretical background in order to attack them. If we couple this with the difficult technical details concerning the corresponding linear problems that are usually needed before one can apply the nonlinear techniques, we find that the student does not come in contact with substantive nonlinear theory until a very advanced stage in his or her studies.