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1. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Dover Books on Mathematics) by Keith B. Oldham, Jerome Spanier | |
Paperback: 234
Pages
(2006-04-28)
list price: US$14.95 -- used & new: US$7.00 (price subject to change: see help) Asin: 0486450015 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Not only does this text explain the theory underlying the properties of the generalized operator, but it also illustrates the wide variety of fields to which these ideas may be applied. Topics include integer order, simple and complex functions, semiderivatives and semiintegrals, and transcendental functions. 1974 edition. Customer Reviews (4)
a good reference, but it could be organized better
A classical book
Excellent book!
Summary : An excellent introduction to the field. This was the first textbook devoted entirely to Fractional Calculus, and remains perhaps the best introduction to the field.It is a graduate level text for mathematicians, engineers and scientists, written in a clear pedagogical style, with excellent references and bibliography. A brief historical survey traces contributions as far back as Leibnitz.Basic results of the traditional integer-order differential and integral calculus are summarized, and properties of some special functions are examined, as a foundation for what follows.Later in the book, many advanced special functions are described in terms of the hypergeometric function. The notions of differentiation and integration are unified as differintegration.Grünwald's definition is presented which extends differintegration to non-integer orders, applicable to functions which satisfy certain conditions.Other definitions used historically are shown to be equivalent to, or special cases of the Grünwald definition.General properties of differintegration are examined, such as linearity and homogeneity.Results corresponding to those of traditional calculus are derived, such as Leibnitz' rule.Significant differences from traditional calculus are also shown, such as the lack of a useful chain rule. The preceding results are illustrated by example, using elementary algebraic, trigonometric, and logarithmic functions, and some special functions, such as hypergeometric, Bessel, and Heaviside.The semiderivative and semiintegral are accorded additional scrutiny, due to their importance in applications.Tables of formulae for semiderivative and semiintegral are provided for elementary functions and common special functions, as well as formulae valid for arbitrary functions.The LaPlace transform or tables of Riemann-Liouville transforms may be used to extend these tables. Practical techniques are presented both for numerical differintegration, suitable for computer implementation, and analog differentegration by means of electrical circuits.Some extraordinary fractional differential equations and semidifferential equations are solved analytically.Techniques of the fractional calculus are applied to a number of well-known problems in traditional calculus, including Abel's equation and Bessel's equation. The diffusion equation and its relatives are treated in a short chapter on practical applications of the fractional calculus.The usual formulations for planar and spherical geometries are examined, including incorporation of sources and sinks, and restriction to finite media. However, the most recent innovations in fractional calculus are not described, such as generalization to complex order.Also, although algorithms for evaluation of differintegrals may be easily derived from the definitions through the book, a set of exemplary pseudocode fragments would be most welcome.These minor flaws are understandable, given the 1974 vintage of the book.A little more material could have been given on Heaviside's Operational Calculus and its relationship to the fractional calculus - it exists only in the references.Similarly, although the link to Weyl calculus is noted, it is not elaborated.Finally, a few examples from rheology would enrich the applications section. COMPARISON : This book covers much the same area as Kenneth Miller and Bertram Ross in "An Introduction to the Fractional Calculus and Fractional Differential Equations", Wiley, 1993. Whereas Oldham and Spanier base their treatise largely on the Grünwald definition, Miller and Ross prefer to use the equivalent Riemann-Liouville definition.Both books contain comparable historical surveys, but Oldham and Spannier provide a more extensive bibliography, and employ a better pedagogical style.Miller and Ross provide results in forms better suited to computer implementation, and rely more on matrix techniques.Also, Miller and Ross provide a chapter on Weyl Calculus, and their practical examples include one from hydrology, but omit diffusion problems.Other than this, the two books share most of their strengths and have only a few weaknesses ... Read more |
2. Schaum's Easy Outline: Calculus by Frank Ayres, Elliott Mendelson | |
Paperback: 135
Pages
(1999-10-11)
list price: US$9.95 -- used & new: US$1.69 (price subject to change: see help) Asin: 0070527105 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description What could be better than the bestselling Schaum's Outline series? For students looking for a quick nuts-and-bolts overview, it would have to be Schaum's Easy Outline series. Every book in this series is a pared-down, simplified, and tightly focused version of its predecessor. With an emphasis on clarity and brevity, each new title features a streamlined and updated format and the absolute essence of the subject, presented in a concise and readily understandable form. Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give students quick pointers to the essentials.
Customer Reviews (3)
Reviewing Kindle edition not book content: almost useless edition
Good for quick review; you still need to do homework. Figures and graphs in the book should help you understand many different problems and how their solutions are derived. You should expect to solve many of the problems in the book yourself, on paper, also. That is the only way to understand mathematics; by doing it yourself. This book should help you get started in the right direction because of the ample examples present in it. Do not expect to get rid your other calculus books and use this as the sole text for reviewing Calculus. This book is meant to be a companion to your other calculus textbooks, not their replacement. As good as it may be, you still need detailed explaination of rules and theories about Calculus, which are not explained in this book.
Outstanding aid to Calculus! |
3. Calculus I: Differentiation and Integration by Dan Hamilton, Linda Hamilton | |
Paperback: 480
Pages
(2002-02)
list price: US$59.95 -- used & new: US$35.86 (price subject to change: see help) Asin: 0964995441 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (1)
Practice, practice, practice... |
4. Schaum's Outline of Calculus for Business, Economics, and The Social Sciences by Edward Dowling | |
Paperback: 288
Pages
(1990-05-01)
list price: US$18.95 -- used & new: US$10.79 (price subject to change: see help) Asin: 0070176736 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
math |
5. Schaum's Outline of Understanding Calculus Concepts by Eli Passow | |
Paperback: 215
Pages
(1996-04-01)
list price: US$18.95 -- used & new: US$5.00 (price subject to change: see help) Asin: 0070487383 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (6)
Schaum's Outline of Understanding Calculus Concepts
Nice for what it has, but a little light on content
A great book
Boring
Quickly guide to understand Calculus |
6. The Integral Calculus: On The Integration Of The Powers Of Transcendental Functions, New Methods And Theorems (1919) by James Ballantyne | |
Hardcover: 46
Pages
(2010-05-23)
list price: US$30.95 -- used & new: US$22.62 (price subject to change: see help) Asin: 116192017X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
7. A Treatise On the Integral Calculus: Containing the Integration of One Variable ; Together with the Theory of Definite Integrals and of Elliptic Functions by John Hymers | |
Paperback: 282
Pages
(2010-04-03)
list price: US$28.75 -- used & new: US$17.08 (price subject to change: see help) Asin: 1148453903 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
8. A Treatise On the Integral Calculus: Containing the Integration of Explicit Functions of One Variable ; Together with the Theory of Definite Integrals and of Elliptic Functions by John Hymers | |
Paperback: 314
Pages
(2010-03-29)
list price: US$29.75 -- used & new: US$17.57 (price subject to change: see help) Asin: 1148120696 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
9. Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces (Contemporary Mathematics) by Topology, and Geometry in Linear Spaces (1979 : University of North Carolina) Conference on Integration, William H. Graves | |
Paperback: 269
Pages
(1980-11)
list price: US$29.00 Isbn: 0821850024 Canada | United Kingdom | Germany | France | Japan | |
10. Calculus for the Utterly Confused by Robert Oman, Daniel Oman | |
Paperback: 208
Pages
(1998-07-01)
list price: US$16.95 -- used & new: US$0.97 (price subject to change: see help) Asin: 0070482616 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (6)
very helpful for refreshing old memory
Good Idea-less than perfect execution
I'm sorry I wasted my money
A handy reference for calculus students.
very helpful |
11. Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering | |
Paperback: 552
Pages
(2010-11-30)
list price: US$219.00 -- used & new: US$173.76 (price subject to change: see help) Asin: 9048175135 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians. |
12. Functional Integration and Its Applications: International Conference Proceedings | |
Hardcover: 176
Pages
(1975-12-11)
Isbn: 0198533462 Canada | United Kingdom | Germany | France | Japan | |
13. The Differential and Integral Calculus: Containing Differentiation, Integration, Development, Series, Differential Equations, Differences, Summation, Equations ... Applications to Algebra, Plan by Augustus De Morgan | |
Paperback: 866
Pages
(2010-06-13)
list price: US$58.75 -- used & new: US$37.68 (price subject to change: see help) Asin: 117453253X Canada | United Kingdom | Germany | France | Japan | |
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14. Schaum's Outline of Calculus (Fourth Edition) by Elliott Mendelson, Frank Ayres | |
Paperback: 578
Pages
(1999-06-28)
list price: US$18.95 -- used & new: US$13.59 (price subject to change: see help) Asin: 0070419736 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (29)
Excellent supplement.
A very good book for studying calculus
Schaum's Outlines are always helpful
Beginner's Calculus
Worth the investment |
15. A Programed Course in Calculus IV, Applications and Techniques of Integration by Editor | |
Paperback: 213
Pages
(1968)
Asin: B000BUIE66 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
16. The differential and integral calculus: Containing differentiation, integration, development, series, differential equations, differences, summation, equations ... of the differential and integral calculus by Augustus De Morgan | |
Hardcover: 785
Pages
(1842)
Asin: B000896HMI Canada | United Kingdom | Germany | France | Japan | |
17. Fractional Calculus: Integrations and Differentiations of Arbitrary Order by Katsuvuki Nishimoto | |
Hardcover:
Pages
(1989-03)
list price: US$70.00 Isbn: 9990036381 Canada | United Kingdom | Germany | France | Japan | |
18. An Introduction to Calculus: Integration I (An Introduction to Calculus) by ANON | |
Paperback: 60
Pages
(1992)
-- used & new: US$55.67 (price subject to change: see help) Asin: 0749220600 Canada | United Kingdom | Germany | France | Japan | |
19. Order of Integration (Calculus) | |
Paperback: 94
Pages
(2010-08-17)
list price: US$44.00 -- used & new: US$41.49 (price subject to change: see help) Asin: 6131296561 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
20. New Trends in Nanotechnology and Fractional Calculus Applications | |
Hardcover: 531
Pages
(2009-12-22)
list price: US$169.00 -- used & new: US$112.88 (price subject to change: see help) Asin: 9048132924 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy. This wide range of applications is of interest to engineers, physicists and mathematicians. |
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