Introduction To Difference Equations (Dover Books On Mathematics)

The highest standards of logical clarity are maintained. — Bulletin of The American Mathematical Society
Written with exceptional lucidity and care, this concise text offers a rigorous introduction to finite differences and difference equations-mathematical tools with widespread applications in the social sciences, economics, and psychology.
The exposition is at an elementary level with little required in the way of mathematical background beyond some facility with standard algebraic techniques and the essentials of trigonometry. Moreover, the author explains when needed such relevant ideas as the function concept, mathematical induction, binomial formula, de Moivre's Theorem and more.
The book begins with a short introductory chapter showing how difference equations arise in the context of social science problems. Chapter One then develops essential parts of the calculus of finite differences. Chapter Two introduces difference equations and some useful applications in the social sciences: compound interest and amortization of debts, the classical Harrod-Domar-Hicks model for growth of national income, Metzler's pure inventory cycle, and others. Chapter Three treats linear differential equations with constant coefficients, including the important question of limiting behavior of solutions, which is discussed and applied to a variety of social science examples. Finally, Chapter Four offers concise coverage of equilibrium values and stability of difference equations, first-order equations and cobweb cycles, and a boundary-value problem. More extensive coverage is devoted to the relatively advanced concepts of generating functions and matrix methods for the solution of systems of simultaneous equations.
Throughout, numerous worked examples and over 250 problems, many with answers, enable students to test their grasp of definitions, theorems and applications. Ideal for an undergraduate course or self-study, this cogent treatment will be of interest to all mathematicians, and especially to social scientists, who will find it an excellent introduction to a powerful tool of theory and research.