This document was prepared in connection with a three-year longitudinal study of career expectations of high school students conducted to explain scientifically the process by which youth form career expectations, e.g., educational, occupational, and income expectations. Divided into six chapters, this document contains a theoretical rationale for a differential equation model of the process by which career expectations of youth evolve and presents a detailed explication of the technical information needed to use the model. Chapter 1 presents the purpose and overview of this report. Chapter 2 contains a theoretical and conceptual discussion of the use of differential equations to represent career planning processes. Chapter 3 presents the basic concepts of selected mathematical and statistical topics, which are discussed in further detail in chapters 4 and 5. Chapter 4 develops the mathematics of differential equations, presents a justification for using ordinary least squares in the statistical analysis, and describes a computer program that can be used to estimate coefficients of the differential equation system. The fifth chapter draws on the technical materials presented in chapters 3 and 4 to describe interpretations of differential equation systems applied to career expectation variables. A summary is presented in Chapter 6. (Author/BM)