MARC details
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05852nam a2200337 a 4500 |
| 001 - ACCESSION NUMBER |
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11145 |
| 003 - CONTROL NUMBER IDENTIFIER |
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CUTN |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20130409115606.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
071113s2008 njua b 001 0 eng d |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
2007046848 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780470270851 (hbk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
0470270853 (hbk.) |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)ocn181335922 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
15078392 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
DLC |
| Transcribing agency |
DLC |
| Modifying agency |
BAKER |
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BTCTA |
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YDXCP |
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C#P |
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BWX |
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CDX |
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AKP |
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SINIE |
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U9S |
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DLC |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA371.5.D37 |
| Item number |
E37 2008 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515/.350285 |
| Edition number |
22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Edsberg, Lennart, |
| Dates associated with a name |
1946- |
| Locally assigned cutter number (author) |
EDS |
| 245 10 - TITLE STATEMENT |
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| Title |
Introduction to computation and modeling for differential equations / |
| Statement of responsibility, etc |
Lennart Edsberg. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Hoboken, N.J. : |
| Name of publisher, distributor, etc |
Wiley, |
| Date of publication, distribution, etc |
c2008. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xvi, 235 p. : |
| Other physical details |
ill. ; |
| Dimensions |
25 cm. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1.1 What is a Differential Equation? -- 1.2 Examples of an ordinary and a partial differential equation. -- 1.3 Numerical analysis, a necessity for scientific computing. -- 1.4 Outline of the contents of this book. -- 2. Ordinary differential equations. -- 2.1 Problem classification. -- 2.2 Linear systems of ODEs with constant coefficients. -- 2.3 Some stability concepts for ODEs. -- 2.3.1 Stability for a solution trajectory of an ODE-system. -- 2.3.2 Stability for critical points of ODE-systems. -- 2.4 Some ODE-models in science and engineering. -- 2.4.1 Newton's second law. -- 2.4.2 Hamilton's equations. -- 2.4.3 Electrical networks. -- 2.4.4 Chemical kinetics. -- 2.4.5 Control theory. -- 2.4.6 Compartment models. -- 2.5 Some examples from applications. -- 3. Numerical methods for IVPs. -- 3.1 Graphical representation of solutions. -- 3.2 Basic principles of numerical approximation of ODEs. -- 3.3 Numerical solution of IVPs with Euler's method. -- 3.3.1 Euler's explicit method: accuracy. -- 3.3.2 Euler's explicit method: improving the accuracy. -- 3.3.3 Euler's explicit method: stability. -- 3.3.4 Euler's implicit method. -- 3.3.5 The trapezoidal method. -- 3.4 Higher order methods for the IVP. -- 3.4.1 Runge-Kutta methods. -- 3.4.2 Linear multistep methods. -- 3.5 The variational equation and parameter fitting in IVPs. -- 3.6 References. -- 4. Numerical methods for BVPs. -- 4.1 Applications. -- 4.2 Difference methods for BVPs. -- 4.2.1 A model problem for BVPs. -- 4.2.2 Accuracy. -- 4.2.3 Spurious oscillations. -- 4.2.4 Linear two-point boundary value problems. -- 4.2.5 Nonlinear two-point boundary value problems. -- 4.2.6 The shooting method. -- 4.3 Ansatz methods for BVPs. -- 5. Partial differential equations. -- 5.1 Classical PDE-problems. -- 5.2 Differential operators used for PDEs. -- 5.3 Some PDEs in science and engineering. -- 5.3.1 Navier-Stokes equations in fluid dynamics. -- 5.3.2 The convection-diffusion-reaction equations. -- 5.3.3 The heat equation. -- 5.3.4 The diffusion equation. -- 5.3.5 Maxwell's equations for the electromagnetic field. -- 5.3.6 Acoustic waves. -- 5.3.7 Schrodinger's equation in quantum mechanics. -- 5.3.8 Navier's equations in structural mechanics. -- 5.3.9 Black-Scholes equation in financial mathematics. -- 5.4 Initial and boundary conditions for PDEs. -- 5.5 Numerical solution of PDEs, some general comments. -- 6. Numerical methods for parabolic PDEs. -- 6.1 Applications. -- 6.2 An introductory example of discretization. -- 6.3 The Method of Lines for parabolic PDEs. -- 6.3.1 Solving the test problem with MoL. -- 6.3.2 Various types of boundary conditions. -- 6.3.3 An example of a mixed BC. -- 6.4 Generalizations of the heat equation. -- 6.4.1 The heat equation with variable conductivity. -- 6.4.2 The convection-diffusion-reaction PDE. -- 6.4.3 The general nonlinear parabolic PDE. -- 6.5 Ansatz methods for the model equation. -- 7. Numerical methods for elliptic PDEs. -- 7.1 Applications. -- 7.2 The Finite Difference Methods. -- 7.3 Discretization of a problem with different BCs. -- 7.4 The Finite Element Method. -- 8. Numerical methods for hyperbolic PDEs. -- 8.1 Applications. -- 8.2 Numerical solution of hyperbolic PDEs. -- 8.3 Introduction to numerical stability for hyperbolic PDEs. -- 9. Mathematical modeling with differential equations. -- 9.1 Nature laws. -- 9.2 Constitutive equations. -- 9.2.1 Equations in heat conduction problems. -- 9.2.2 Equations in mass diffusion problems. -- 9.2.3 Equations in mechanical moment diffusion problems. -- 9.2.4 Equations in elastic solid mechanics problems. -- 9.2.5 Equations in chemical reaction engineering problems. -- 9.2.6 Equations in electrical engineering problems. -- 9.3 Conservative equations. -- 9.3.1 Some examples of lumped models. -- 9.3.2 Some examples of distributed models. -- 9.4 Scaling of differential equations to dimensionless form. -- A. Appendix. -- A.1 Newton's method for systems of nonlinear algebraic equations. -- A.1.1 Quadratic systems. -- A.1.2 Overdetermined systems. -- A.2 Some facts about linear difference equations. -- A.3 Derivation of difference approximations. -- A.4 The interpretations of div and curl. -- A.5 Numerical solution of algebraic systems of equations. -- A.5.1 Direct methods. -- A.5.2 Iterative methods for linear systems of equations. -- A.6 Some results for Fourier transforms. -- B. Software for scientific computing. -- B.1 Matlab. -- B.2 Comsol Multiphysics. -- C. Computer exercises to support the chapters. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Differential equations |
| General subdivision |
Data processing. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Differential equations |
| General subdivision |
Mathematical models. |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Contributor biographical information |
| Uniform Resource Identifier |
<a href="http://www.loc.gov/catdir/enhancements/fy0829/2007046848-b.html">http://www.loc.gov/catdir/enhancements/fy0829/2007046848-b.html</a> |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Publisher description |
| Uniform Resource Identifier |
<a href="http://www.loc.gov/catdir/enhancements/fy0806/2007046848-d.html">http://www.loc.gov/catdir/enhancements/fy0806/2007046848-d.html</a> |
| 856 41 - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Table of contents only |
| Uniform Resource Identifier |
<a href="http://www.loc.gov/catdir/enhancements/fy0806/2007046848-t.html">http://www.loc.gov/catdir/enhancements/fy0806/2007046848-t.html</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
General Books |
