| Difference Equations appear as convenient descriptions of discrete mathematical models. The application of the theory of difference equations is rapidly gaining importance in various fields such as numerical analysis, control theory, finite mathematics, and computer science. In our thesis we "emphasize" showing examples and proving some important results in the theory of difference equations. In chapter-I, we introduce the theory of finite calculus. We introduce the operators in difference calculus, prove the product and quotient rules for differences of functions, and describe the tabular technique of finite integration by parts. In chapter-II, we present the terminology and method of solving linear difference equations by means of examples. Chapter-III deals with systems of difference equations. We also prove properties of fundamental matrices and show examples of solving linear systems. In chapter-IV, we present stability notions of linear and nonlinear systems of difference equations. Finally in chapter-V, we prove some of the properties of Z-transforms and show examples of solving linear difference equations using Z-transform method. |
