Linear Difference Equations with Discrete Transform Methods

1. Front Matter

   Pages i-xxi

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2. Sequences and Difference Operators

   • Abdul J. Jerri

   Pages 1-40

3. Sum Calculus and the Discrete Transforms Methods

   • Abdul J. Jerri

   Pages 41-137

4. Basic Methods of Solving Linear Difference Equations

   • Abdul J. Jerri

   Pages 139-280

5. Discrete Fourier Transforms

   • Abdul J. Jerri

   Pages 281-328

6. The Discrete Sine (DST) and Cosine (DCT) Transforms for Boundary Value Problems

   • Abdul J. Jerri

   Pages 329-353

7. The z-Transform for Initial Value Problems

   • Abdul J. Jerri

   Pages 355-383

8. Modeling with Difference Equations

   • Abdul J. Jerri

   Pages 385-404

9. Back Matter

   Pages 405-442

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This book covers the basic elements of difference equations and the tools of difference and sum calculus necessary for studying and solv­ 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 in­ tended mainly as a text for the beginning undergraduate course in difference equations, where the "operational sum calculus" of the di­ 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 meth­ 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 solv­ ing ordinary difference equations. The treatment closely parallels what many students have already learned about using the opera­ 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 meth­ 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 eas­ ily to solve partial difference equations associated with initial and/or boundary value problems.

• Boundary value problem
• Fourier transform
• calculus
• difference equation
• discrete Fourier transform
• modeling
• operator

• Clarkson University, USA

  Abdul J. Jerri

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