MARC ayrıntıları
| 000 -LEADER |
|---|
| fixed length control field |
05418nam a2200313 i 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
|---|
| fixed length control field |
100415s2010 enka b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781848163294 |
| Qualifying information |
(hardback) |
|
|---|
| International Standard Book Number |
1848163290 |
| Qualifying information |
(hardback) |
| 040 ## - CATALOGING SOURCE |
|---|
| Original cataloging agency |
UKM |
| Language of cataloging |
eng |
| Transcribing agency |
UKM |
| Modifying agency |
BWK |
| -- |
YDXCP |
| -- |
BTCTA |
| -- |
C#P |
| -- |
BWX |
| -- |
UtOrBLW |
| -- |
BAUN |
| Description conventions |
rda |
| 049 ## - LOCAL HOLDINGS (OCLC) |
|---|
| Holding library |
BAUN_MERKEZ |
| 050 04 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA314 |
| Item number |
.M35 2010 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Edition number |
22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Mainardi, F. |
| Fuller form of name |
(Francesco), |
| Dates associated with a name |
1942- |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Fractional calculus and waves in linear viscoelasticity : |
| Remainder of title |
an introduction to mathematical models / |
| Statement of responsibility, etc |
Francesco Mainardi |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
|---|
| Place of production, publication, distribution, manufacture |
London ; |
| -- |
Hackensack, NJ : |
| Name of producer, publisher, distributor, manufacturer |
Imperial College Press, |
| Date of production, publication, distribution, manufacture, or copyright notice |
[2010] |
|
|---|
| Date of production, publication, distribution, manufacture, or copyright notice |
©2010 |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
xx, 347 pages : |
| Other physical details |
illustrations ; |
| Dimensions |
24 cm |
| 336 ## - CONTENT TYPE |
|---|
| Content Type Term |
text |
| Content Type Code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
|---|
| Media Type Term |
unmediated |
| Media Type Code |
unmediated |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
|---|
| Carrier Type Term |
volume |
| Carrier Type Code |
volume |
| Source |
rdacarrier |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc |
Includes bibliographical references and index |
| 505 00 - FORMATTED CONTENTS NOTE |
|---|
| Title |
Contents |
| -- |
Preface |
| -- |
Acknowledgements |
| -- |
List of Figures |
| -- |
1 Essentials of Fractional Calculus |
| -- |
1.1 The fractional integral with support in IR+ |
| -- |
1.2 The fractional derivative with support in IR+ |
| -- |
1.3 Fractional relaxation equations in IR+ |
| -- |
1.4 Fractional integrals and derivatives with support in IR |
| -- |
1.5 Notes |
| -- |
2 Essentials of Linear Viscoelasticity |
| -- |
2.1 Introduction |
| -- |
2.2 History in IR+: the Laplace transform approach |
| -- |
2.3 The four types of viscoelasticity |
| -- |
2.4 The classical mechanical models |
| -- |
2.5 The time - and frequency - spectral functions |
| -- |
2.6 History in IR: the Fourier transform approach and the dynamic functions |
| -- |
2.7 Storage and dissipation of energy: the loss tangent |
| -- |
2.8 The dynamic functions for the mechanical models |
| -- |
2.9 Notes |
| -- |
3 Fractional Viscoelastic Models |
| -- |
3.1 The fractional calculus in the mechanical models |
| -- |
3.1.1 Power-Law creep and the Scott-Blair model |
| -- |
3.1.2 The correspondence principle |
| -- |
3.1.3 The fractional mechanical models |
| -- |
3.2 Analysis of the fractional Zener model |
| -- |
3.2.1 The material and the spectral functions |
| -- |
3.2.2 Dissipation: theoretical considerations |
| -- |
3.2.3 Dissipation: experimental checks |
| -- |
3.3 The physical interpretation of the fractional Zener model via fractional diffusion |
| -- |
3.4 Which type of fractional derivative? Caputo or Riemann-Liouville? |
| -- |
3.5 Notes |
| -- |
4 Waves in Linear Viscoelastic Media: Dispersion and Dissipation |
| -- |
4.1 Introduction |
| -- |
4.2 Impact waves in linear viscoelasticity |
| -- |
4.2.1 Statement of the problem by Laplace transforms |
| -- |
4.2.2 The structure of wave equations in the space-time domain |
| -- |
4.2.3 Evolution equations for the mechanical models |
| -- |
4.3 Dispersion relation and complex refraction index |
| -- |
4.3.1 Generalities |
| -- |
4.3.2 Dispersion: phase velocity and group velocity |
| -- |
4.3.3 Dissipation: the attenuation coefficient and the specific dissipation function |
| -- |
4.3.4 Dispersion and attenuation for the Zener and the Maxwell models |
| -- |
4.3.5 Dispersion and attenuation for the fractional Zener model |
| -- |
4.3.6 The Klein-Gordon equation with dissipation |
| -- |
4.4 The Brillouin signal velocity |
| -- |
4.4.1 Generalities |
| -- |
4.4.2 Signal velocity via steepest-descent path |
| -- |
4.5 Notes |
| -- |
5 Waves in Linear Viscoelastic Media: Asymptotic Representations |
| -- |
5.1 The regular wave-front expansion |
| -- |
5.2 The singular wave-front expansion |
| -- |
5.3 The saddle-point approximation |
| -- |
5.3.1 Generalities |
| -- |
5.3.2 The Lee-Kanter problem for the Maxwell model |
| -- |
5.3.3 The Jeffreys problem for the Zener model |
| -- |
5.4 The matching between the wave-front and the saddle-point approximations |
| -- |
6 Diffusion and Wave-Propagation via Fractional Calculus |
| -- |
6.1 Introduction |
| -- |
6.2 Derivation of the fundamental solutions |
| -- |
6.3 Basic properties and plots of the Green functions |
| -- |
6.4 The Signalling problem in a viscoelastic solid with a power-law creep |
| -- |
6.5 Notes |
| -- |
Appendix A The Eulerian Functions |
| -- |
A.1 The Gamma function: Γ(z) |
| -- |
A.2 The Beta function: B(p, q) |
| -- |
A.3 Logarithmic derivative of the Gamma function |
| -- |
A.4 The incomplete Gamma functions |
| -- |
Appendix B The Bessel Functions |
| -- |
B.1 The standard Bessel functions |
| -- |
B.2 The modified Bessel functions |
| -- |
B.3 Integral representations and Laplace transforms |
| -- |
B.4 The Airy functions |
| -- |
Appendix C The Error Functions |
| -- |
C.1 The two standard Error functions |
| -- |
C.2 Laplace transform pairs |
| -- |
C.3 Repeated integrals of the Error functions |
| -- |
C.4 The Erfi function and the Dawson integral |
| -- |
C.5 The Fresnel integrals |
| -- |
Appendix D The Exponential Integral Functions |
| -- |
D.1 The classical Exponential integrals Ei(z), ε1(z) |
| -- |
D.2 The modified Exponential integral Ein (z) |
| -- |
D.3 Asymptotics for the Exponential integrals |
| -- |
D.4 Laplace transform pairs for Exponential integrals |
| -- |
Appendix E The Mittag-Leffler Functions |
| -- |
E.1 The classical Mittag-Leffler function Ea(z) |
| -- |
E.2 The Mittag-Leffler function with two parameters |
| -- |
E.3 Other functions of the Mittag-Leffler type |
| -- |
E.4 The Laplace transform pairs |
| -- |
E.5 Derivatives of the Mittag-Leffler functions |
| -- |
E.6 Summation and integration of Mittag-Leffler functions |
| -- |
E.7 Applications of the Mittag-Leffler functions to the Abel integral equations |
| -- |
E.8 Notes |
| -- |
Appendix F The Wright Functions |
| -- |
F.1 The Wright function Wλ,μ(z) |
| -- |
F.2 The auxiliary functions Fv(z) and Mv(z) in C |
| -- |
F.3 The auxiliary functions Fv(x) and Mv(x) in IR |
| -- |
F.4 The Laplace transform pairs |
| -- |
F.5 The Wright M-functions in probability |
| -- |
F.6 Notes |
| -- |
Bibliography |
| -- |
Index |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Fractional calculus |
|
|---|
| Topical term or geographic name as entry element |
Waves |
| General subdivision |
Mathematical models |
|
|---|
| Topical term or geographic name as entry element |
Viscoelasticity |
| General subdivision |
Mathematical models |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| 9 (RLIN) |
28005 |
| Corporate name or jurisdiction name as entry element |
Imperial College Press. |
| 900 ## - EQUIVALENCE OR CROSS-REFERENCE-PERSONAL NAME [LOCAL, CANADA] |
|---|
| Personal Name |
31266 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
Library of Congress Classification |
| Koha item type |
Kitap |
-baunlogo.png?alt=media&token=2b1f50b7-298a-48ee-a2b1-6fcf8e70b387)
-Facebook-2024.png?alt=media&token=2fcc0655-0091-431c-8ee0-059464d6eda1){kind=small}
-Instagram-2024.png?alt=media&token=a143a92a-6f9d-45a7-9ba2-9cc62f92e772){kind=small}