MARC ayrıntıları
| 000 -LEADER |
|---|
| fixed length control field |
06514nam a2200253 i 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
|---|
| fixed length control field |
130716s2013 si m b a001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9789814407564 |
|
|---|
| International Standard Book Number |
9814407569 |
| 040 ## - CATALOGING SOURCE |
|---|
| Original cataloging agency |
BAUN |
| Language of cataloging |
eng |
| Transcribing agency |
BAUN |
| Description conventions |
rda |
| 049 ## - LOCAL HOLDINGS (OCLC) |
|---|
| Holding library |
BAUN_MERKEZ |
| 050 04 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA374 |
| Item number |
.H38 2013 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Hattori, Harumi. |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Partial differential equations : |
| Remainder of title |
methods, applications and theories / |
| Statement of responsibility, etc |
Harumi Hattori. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
|---|
| Place of production, publication, distribution, manufacture |
Singapore : |
| Name of producer, publisher, distributor, manufacturer |
World Scientific Publishing, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2013. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
375 pages : |
| Other physical details |
illustrations ; |
| Dimensions |
26 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 (pages 369-370) and index. |
| 505 00 - FORMATTED CONTENTS NOTE |
|---|
| Title |
Table Of Contents: |
| -- |
Preface |
| -- |
1 First and Second Order Linear Equations - Preparation |
| -- |
1.1 Terminologies |
| -- |
1.2 Linearity |
| -- |
1.2.1 Superposition Principle |
| -- |
1.2.2 Linear Independence |
| -- |
1.3 First Order Linear Equations |
| -- |
1.3.1 Initial Value Problems |
| -- |
1.3.2 General Solutions |
| -- |
1.4 Classification of Second Order Linear Equations |
| -- |
1.5 Well-posedness |
| -- |
2 Heat Equation |
| -- |
2.1 Derivation of the Heat Equation |
| -- |
2.1.1 One-dimensional Case |
| -- |
2.1.2 Divergence Theorem |
| -- |
2.1.3 Multi-dimensional Case |
| -- |
2.2 Initial Boundary Value Problems |
| -- |
2.3 Homogeneous Boundary Conditions |
| -- |
2.3.1 Temperature is Fixed at Zero at Both Ends |
| -- |
2.3.2 Brief Discussion of the Fourier Series |
| -- |
2.3.3 Both Ends are Insulated |
| -- |
2.3.4 Temperature of One End is Zero and the Other End is Insulated |
| -- |
2.4 Non-homogeneous Boundary Conditions |
| -- |
2.4.1 Steady State Solutions |
| -- |
2.4.2 Non-homogeneous Boundary Conditions |
| -- |
2.5 Robin Boundary Conditions |
| -- |
2.6 Infinite Domain Problems |
| -- |
2.6.1 Initial Value Problems |
| -- |
2.6.2 Initial Value Problems via Fourier Transform |
| -- |
2.6.3 Semi-infinite Domains |
| -- |
2.7 Maximum Principle, Energy Method, and Uniqueness of Solutions |
| -- |
2.7.1 Maximum Principle |
| -- |
2.7.2 Energy Method |
| -- |
3 Wave Equation |
| -- |
3.1 Derivation of Wave Equation |
| -- |
3.1.1 One-dimensional Case |
| -- |
3.1.2 Multi-dimensional Case |
| -- |
3.2 Initial Value Problems |
| -- |
3.2.1 Homogeneous Wave Equation |
| -- |
3.2.2 Non-homogeneous Wave Equation |
| -- |
3.3 Wave Reflection Problems |
| -- |
3.3.1 Homogeneous Boundary Conditions |
| -- |
3.3.2 Non-homogeneous Boundary Conditions |
| -- |
3.4 Initial Boundary Value Problems |
| -- |
3.5 Energy Method |
| -- |
4 Laplace Equation |
| -- |
4.1 Motivations |
| -- |
4.2 Boundary Value Problems - Separation of Variables |
| -- |
4.2.1 Laplace Equation on a Rectangular Domain |
| -- |
4.2.2 Laplace Equation on a Circular Disk |
| -- |
4.3 Fundamental Solution |
| -- |
4.3.1 Green's Identity |
| -- |
4.3.2 Derivation of Fundamental Solution |
| -- |
4.3.3 Green's Identity and Fundamental Solution |
| -- |
4.4 Green's Function |
| -- |
4.4.1 Definition |
| -- |
4.4.2 Green's Function for a Half Space |
| -- |
4.4.3 Green's Function for a Ball |
| -- |
4.4.4 Symmetry of Green's Function |
| -- |
4.5 Properties of Harmonic Functions |
| -- |
4.5.1 Mean Value Property |
| -- |
4.5.2 The Maximum Principle and Uniqueness |
| -- |
4.6 Well-posedness Issues |
| -- |
4.6.1 Laplace Equation |
| -- |
4.6.2 Wave Equation |
| -- |
5 First Order Equations Revisited |
| -- |
5.1 First Order Quasilinear Equations |
| -- |
5.2 An Application of Quasilinear Equations |
| -- |
5.2.1 Scalar Conservation Law |
| -- |
5.2.2 Rankine-Hugoniot Condition |
| -- |
5.2.3 Weak Solutions |
| -- |
5.2.4 Entropy Condition and Admissibility Criterion |
| -- |
5.2.5 Traffic Flow Problem |
| -- |
5.3 First Order Nonlinear Equations |
| -- |
5.4 An Application of Nonlinear Equations - Optimal Control Problem |
| -- |
5.5 Systems of First Order Equations |
| -- |
5.5.1 2 x 2 System |
| -- |
5.5.2 n x n System |
| -- |
6 Fourier Series and Eigenvalue Problems |
| -- |
6.1 Even, Odd, and Periodic Functions |
| -- |
6.1.1 Even and Odd Functions |
| -- |
6.1.2 Periodic Functions |
| -- |
6.2 Fourier Series |
| -- |
6.2.1 Fourier Series |
| -- |
6.2.2 Fourier Sine and Cosine Series |
| -- |
6.3 Fourier Convergence Theorems |
| -- |
6.3.1 Mean-square Convergence |
| -- |
6.3.2 Pointwise Convergence |
| -- |
6.3.3 Uniform Convergence |
| -- |
6.4 Derivatives of Fourier Series |
| -- |
6.5 Eigenvalue Problems |
| -- |
6.5.1 The Sturm-Liouville Problems |
| -- |
6.5.2 Proofs |
| -- |
7 Separation of Variables in Higher Dimensions |
| -- |
7.1 Rectangular Domains |
| -- |
7.2 Eigenvalue Problems |
| -- |
7.2.1 Multidimensional Case |
| -- |
7.2.2 Gram-Schmidt Orthogonalization Procedure |
| -- |
7.2.3 Rayleigh Quotient |
| -- |
7.3 Eigenfunction Expansions |
| -- |
7.3.1 Non-homogeneous Boundary Conditions |
| -- |
7.3.2 Homogeneous Boundary Conditions |
| -- |
7.3.3 Hybrid Method |
| -- |
8 More Separation of Variables |
| -- |
8.1 Circular Domains |
| -- |
8.1.1 Initial Boundary Value Problems |
| -- |
8.1.2 Bessel and Modified Bessel Functions |
| -- |
8.2 Cylindrical Domains |
| -- |
8.2.1 Initial Boundary Value Problems |
| -- |
8.2.2 Laplace Equation |
| -- |
8.3 Spherical Domains |
| -- |
8.3.1 Initial Boundary Value Problems |
| -- |
8.3.2 Legendre Equation |
| -- |
8.3.3 Laplace Equation |
| -- |
9 Fourier Transform |
| -- |
9.1 Delta Functions |
| -- |
9.1.1 Classical Introduction |
| -- |
9.1.2 Modern Introduction |
| -- |
9.2 Fourier Transform |
| -- |
9.2.1 Complex Form of the Fourier Series |
| -- |
9.2.2 Fourier Transform and Inverse |
| -- |
9.3 Properties of Fourier Transform |
| -- |
9.3.1 Fourier Transform of Derivatives |
| -- |
9.3.2 Convolution |
| -- |
9.3.3 Plancherel Formula |
| -- |
9.4 Applications of Fourier Transform |
| -- |
9.4.1 Heat Equation |
| -- |
9.4.2 Wave Equation |
| -- |
9.4.3 Laplace Equation in a Half Space |
| -- |
9.4.4 Black-Scholes-Merton Equation |
| -- |
10 Laplace Transform |
| -- |
10.1 Laplace Transform and the Inverse |
| -- |
10.1.1 Laplace Transform |
| -- |
10.1.2 Inverse Transform |
| -- |
10.2 Properties of the Laplace Transform |
| -- |
10.2.1 Laplace Transform of Derivatives |
| -- |
10.2.2 Convolution Theorem |
| -- |
10.2.3 Relation with the Fourier Transform |
| -- |
10.3 Applications to Differential Equations |
| -- |
10.3.1 Applications to ODE's |
| -- |
10.3.2 Applications to PDE's |
| -- |
11 Higher Dimensional Problems - Other Approaches |
| -- |
11.1 Spherical Means and Method of Descent |
| -- |
11.1.1 Method of Spherical Means |
| -- |
11.1.2 The Method of Descent |
| -- |
11.2 Duhamel's Principle |
| -- |
11.2.1 Heat Equation |
| -- |
11.2.2 Wave Equation |
| -- |
12 Green's Functions |
| -- |
12.1 Green's Functions for the Laplace Equation |
| -- |
12.1.1 Eigenfunction Expansion |
| -- |
12.1.2 Modified Green's Function |
| -- |
12.2 Green's Functions for the Heat Equation |
| -- |
12.2.1 Initial Boundary Value Problems |
| -- |
12.2.2 Initial Value Problems |
| -- |
12.3 Green's Functions for the Wave Equation |
| -- |
12.3.1 Initial Boundary Value Problems |
| -- |
12.3.2 Initial Value Problems |
| -- |
Appendices |
| -- |
A.1 Exchanging the Order of Integration and Differentiation |
| -- |
A.2 Infinite Series |
| -- |
A.3 Useful Formulas in ODE's |
| -- |
A.3.1 First Order Linear Equations |
| -- |
A.3.2 Bernoulli Equations |
| -- |
A.3.3 Second Order Linear Constant Coefficient Equations |
| -- |
A.3.4 Variation of Parameters Formula |
| -- |
A.4 Linear Algebra |
| -- |
A.4.1 Solutions to Systems of Linear Equations |
| -- |
A.4.2 Eigenvalues, Eigenvectors, and Diagonalization |
| -- |
Hints and Solutions to Selected Exercises |
| -- |
Bibliography |
| -- |
Index |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Differential equations, Partial. |
| 900 ## - EQUIVALENCE OR CROSS-REFERENCE-PERSONAL NAME [LOCAL, CANADA] |
|---|
| Personal Name |
34873 |
| 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}