Buch, Englisch, 442 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 703 g
Buch, Englisch, 442 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 703 g
Reihe: Mathematics and Its Applications
ISBN: 978-1-4419-4755-0
Verlag: Springer US
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
Weitere Infos & Material
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.
