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AuthorJerri, Abdul J. author
TitleLinear Difference Equations with Discrete Transform Methods [electronic resource] / by Abdul J. Jerri
ImprintBoston, MA : Springer US : Imprint: Springer, 1996
Connect tohttp://dx.doi.org/10.1007/978-1-4757-5657-9
Descript XXI, 442 p. online resource

SUMMARY

This book covers the basic elements of difference equations and the tools of difference and sum calculus necessary for studying and solvยญ ing, primarily, ordinary linear difference equations. Examples from various fields are presented clearly in the first chapter, then discussed along with their detailed solutions in Chapters 2-7. The book is inยญ tended mainly as a text for the beginning undergraduate course in difference equations, where the "operational sum calculus" of the diยญ rect use of the discrete Fourier transforms for solving boundary value problems associated with difference equations represents an added new feature compared to other existing books on the subject at this introductory level. This means that in addition to the familiar methยญ ods of solving difference equations that are covered in Chapter 3, this book emphasizes the use of discrete transforms. It is an attempt to introduce the methods and mechanics of discrete transforms for solvยญ ing ordinary difference equations. The treatment closely parallels what many students have already learned about using the operaยญ tional (integral) calculus of Laplace and Fourier transforms to solve differential equations. As in the continuous case, discrete operational methods may not solve problems that are intractable by other methยญ ods, but they can facilitate the solution of a large class of discrete initial and boundary value problems. Such operational methods, or what we shall term "operational sum calculus," may be extended easยญ ily to solve partial difference equations associated with initial and/or boundary value problems


CONTENT

1 Sequences and Difference Operators -- 2 Sum Calculus and the Discrete Transforms Methods -- 3 Basic Methods of Solving Linear Difference Equations -- 4 Discrete Fourier Transforms -- 5 The Discrete Sine (DST) and Cosine (DCT) Transforms for Boundary Value Problems -- 6 The z-Transform for Initial Value Problems -- 7 Modeling with Difference Equations -- References -- Answers to Exercises -- Index of Notations


Mathematics Difference equations Functional equations Integral transforms Operational calculus Computer mathematics Mathematical models Mathematics Difference and Functional Equations Computational Mathematics and Numerical Analysis Integral Transforms Operational Calculus Mathematical Modeling and Industrial Mathematics



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