Introduction to Difference Equations

Samuel Goldberg

Introduction to Difference Equations is written with exceptional clarity and care and offers a rigorous introduction to finite differences and difference equations. Finite differences and difference equations are mathematical tools that have widespread applications in the social sciences, economics, and psychology.

The presentation is on an elementary level, and the necessary mathematical background is little. You should have some proficiency with common algebraic techniques and the fundamentals of trigonometry, but that is about it. In addition, the author will, when necessary, explain concepts as important as the function notion, mathematical induction, the binomial formula, de Moivre’s Theorem, and other concepts.

The first chapter of this book is an introductory one, only a few pages long, explaining how different equations can be used for social science issues. After that, the fundamental aspects of the calculus of finite differences are developed in chapter one.

In Chapter Two, Difference Equations are Introduced, along with several Useful Applications in the Social Sciences. These Applications Include Compound Interest and Amortization of Debts, the Classical Harrod-Domar-Hicks Model for Growth of National Income, Metzler’s Pure Inventory Cycle, and Others. In the third chapter, linear differential equations with constant coefficients are explored. This includes the crucial topic of limiting the behavior of solutions, which is then applied to several different social science cases.

In conclusion, the fourth chapter provides a succinct overview of equilibrium values, the stability of difference equations, first-order equations, cobweb cycles, and a boundary-value problem. The relatively sophisticated ideas of generating functions and matrix approaches for solving systems of simultaneous equations are discussed in further detail in this chapter.

Students are allowed to test their understanding of definitions, theorems, and applications throughout the text through multiple worked examples and over 250 problems, many of which include answers. This clear presentation is well-suited for either a college-level class or independent study. It will pique the curiosity of not only mathematicians but also social scientists, for whom it will serve as an outstanding introduction to a powerful method that may be used in both theory and research.