國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Discrete fractional calculus

Goodrich, Christopher.

Discrete fractional calculus

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Discrete fractional calculusby Christopher Goodrich, Allan C. Peterson.
作者:	Goodrich, Christopher.
其他作者:	Peterson, Allan C.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xiii, 556 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Fractional calculus.
電子資源:	http://dx.doi.org/10.1007/978-3-319-25562-0
ISBN:	9783319255620$q(electronic bk.)

Discrete fractional calculus
Goodrich, Christopher.

Discrete fractional calculus[electronic resource] /by Christopher Goodrich, Allan C. Peterson. - Cham :Springer International Publishing :2015. - xiii, 556 p. :ill., digital ;24 cm.

Preface -- 1. Basic Difference Calculus -- 2. Discrete Delta Fractional Calculus and Laplace Transforms -- 3. Nabla Fractional Calculus -- 4. Quantum Calculus -- 5. Calculus on Mixed Time Scales -- 6. Fractional Boundary Value Problems -- 7. Nonlocal BVPs and the Discrete Fractional Calculus -- Solutions to Selected Problems -- Bibliography -- Index.

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. 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.

ISBN: 9783319255620$q(electronic bk.)

Standard No.: 10.1007/978-3-319-25562-0doiSubjects--Topical Terms:

208302
Fractional calculus.

LC Class. No.: QA314

Dewey Class. No.: 515.83

Discrete fractional calculus
LDR:03257nmm a2200313 a 4500 001 477877
003 DE-He213
005 20160527133515.0
006 m d
007 cr nn 008maaau
008 160614s2015 gw s 0 eng d
020 $a 9783319255620$q(electronic bk.)
020 $a 9783319255606$q(paper)
024 7 $a 10.1007/978-3-319-25562-0 $2 doi
035 $a 978-3-319-25562-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA314
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
082 0 4 $a 515.83 $2 23
090 $a QA314 $b .G654 2015
100 1 $a Goodrich, Christopher. $3 732900
245 1 0 $a Discrete fractional calculus $h [electronic resource] / $c by Christopher Goodrich, Allan C. Peterson.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xiii, 556 p. : $b ill., digital ; $c 24 cm.
505 0 $a Preface -- 1. Basic Difference Calculus -- 2. Discrete Delta Fractional Calculus and Laplace Transforms -- 3. Nabla Fractional Calculus -- 4. Quantum Calculus -- 5. Calculus on Mixed Time Scales -- 6. Fractional Boundary Value Problems -- 7. Nonlocal BVPs and the Discrete Fractional Calculus -- Solutions to Selected Problems -- Bibliography -- Index.
520 $a This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. 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.
650 0 $a Fractional calculus. $3 208302
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Ordinary Differential Equations. $3 273778
650 2 4 $a Difference and Functional Equations. $3 274826
650 2 4 $a Real Functions. $3 273779
700 1 $a Peterson, Allan C. $3 188254
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-25562-0
950 $a Mathematics and Statistics (Springer-11649)