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The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the subject.
Most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as a primary reference in an introductory course for difference equations which also includes discrete fractional calculus. Chapters 1¿2 provide a basic introduction to the delta calculus including fractional calculus on the set of integers. For courses where students already have background in elementary real analysis, Chapters 1¿2 may be covered quickly and readers may then skip to Chapters 6¿7 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6¿7 in conjunction with some of the current literature listed in the Bibliography can provide a basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1¿5 may be covered in depth, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order calculus.
The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the subject.
Most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as a primary reference in an introductory course for difference equations which also includes discrete fractional calculus. Chapters 1¿2 provide a basic introduction to the delta calculus including fractional calculus on the set of integers. For courses where students already have background in elementary real analysis, Chapters 1¿2 may be covered quickly and readers may then skip to Chapters 6¿7 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6¿7 in conjunction with some of the current literature listed in the Bibliography can provide a basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1¿5 may be covered in depth, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order calculus.
Christopher Goodrich is currently a mathematics instructor at the Creighton Preparatory School in Omaha, Nebraska.
May be used for courses at the upper undergraduate level and above; the field is promoted by specialists
Flexibility in its use, the text covers all aspects of discrete functional calculus
Contains good examples, suitable problems, and comprehensive coverage of the topic
Includes supplementary material: [...]
Erscheinungsjahr: | 2018 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
Seiten: | 572 |
Inhalt: |
xiii
556 S. |
ISBN-13: | 9783319798097 |
ISBN-10: | 331979809X |
Sprache: | Englisch |
Ausstattung / Beilage: | Paperback |
Einband: | Kartoniert / Broschiert |
Autor: |
Peterson, Allan C.
Goodrich, Christopher |
Auflage: | Softcover reprint of the original 1st ed. 2015 |
Hersteller: |
Springer International Publishing
Springer International Publishing AG |
Maße: | 235 x 155 x 31 mm |
Von/Mit: | Allan C. Peterson (u. a.) |
Erscheinungsdatum: | 30.03.2018 |
Gewicht: | 0,855 kg |
Christopher Goodrich is currently a mathematics instructor at the Creighton Preparatory School in Omaha, Nebraska.
May be used for courses at the upper undergraduate level and above; the field is promoted by specialists
Flexibility in its use, the text covers all aspects of discrete functional calculus
Contains good examples, suitable problems, and comprehensive coverage of the topic
Includes supplementary material: [...]
Erscheinungsjahr: | 2018 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
Seiten: | 572 |
Inhalt: |
xiii
556 S. |
ISBN-13: | 9783319798097 |
ISBN-10: | 331979809X |
Sprache: | Englisch |
Ausstattung / Beilage: | Paperback |
Einband: | Kartoniert / Broschiert |
Autor: |
Peterson, Allan C.
Goodrich, Christopher |
Auflage: | Softcover reprint of the original 1st ed. 2015 |
Hersteller: |
Springer International Publishing
Springer International Publishing AG |
Maße: | 235 x 155 x 31 mm |
Von/Mit: | Allan C. Peterson (u. a.) |
Erscheinungsdatum: | 30.03.2018 |
Gewicht: | 0,855 kg |