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The authors have worked together since 1984 on the development and application of difference equations. Sometimes our work was episodic, at other times it was continuous. Sometimes we published in the peer reviewed literature while at other times we wrote only for ourselves. Sometimes we taught, and at other times, we merely talked. Difference equations have provided a consistent cadence for us, the background beat to which our careers unconsciously moved. For each of us, difference equations have held a fascination in and of themselves, and it has always been natural for the two of us to immerse ourselves in their solution to the exclusion of all else. However, working in a school of public health means involvement in public health issues. We have committed to continually explore the possibility of linking difference equations to public health topics. Issues in public health, whether environmental, economic, or patient-care oriented, involve a host of interdependencies which we suspected might be clearly reflected in families of difference equations.
A familiar medical school adage is that physicians cannot diagnose a disease they know nothing about. Similarly, quantitative students in publichealth cannot consider utilizing difference equations to formulate a public health problem unless they are comfortable with their formulations and solutions. Difference equations have been the focus of attention by several authors including Samuel Goldberg's classic text, Introduction to Difference Equations, published in 1958. However, none of these have focused on the use of difference equations in public health. Although generating functions cannot be used to solve every difference equation, we have chosen to elevate them to the primary tool. Mastering these tools provides a path to the solution of complicated difference equations.
We would like to express our appreciation and thanks to Ms. Kathleen Baldonado for her valuable suggestions, extraordinary editing efforts, and keeping these turbulent authors calm.
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