Volterra integral and differential equations /:
Volterra integral and differential equations.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Academic Press,
1983.
|
| Schriftenreihe: | Mathematics in science and engineering ;
v. 167. |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Zusammenfassung: | Volterra integral and differential equations. |
| Beschreibung: | 1 online resource (x, 313 pages) |
| Bibliographie: | Includes bibliographical references (pages 303-307) and indexes. |
| ISBN: | 9780080956732 0080956734 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn316566646 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 090320s1983 nyu ob 001 0 eng d | ||
| 040 | |a OPELS |b eng |e pn |c OPELS |d N$T |d OCLCQ |d EBLCP |d IDEBK |d OPELS |d E7B |d OCLCQ |d OPELS |d OCLCQ |d UIU |d OCLCQ |d OCLCO |d OCLCQ |d OCLCF |d DEBBG |d OCLCQ |d NLGGC |d UIU |d DEBSZ |d YDXCP |d OCLCQ |d AGLDB |d OCLCQ |d VTS |d STF |d LEAUB |d M8D |d OCLCQ |d OCLCO |d SGP |d INARC |d OCLCQ |d OCLCO |d OCLCL | ||
| 019 | |a 646827534 |a 742295384 |a 816325397 |a 823122218 |a 823843629 |a 823912396 |a 824099400 |a 824154823 | ||
| 020 | |a 9780080956732 |q (electronic bk.) | ||
| 020 | |a 0080956734 |q (electronic bk.) | ||
| 020 | |z 9780121473808 | ||
| 020 | |z 0121473805 | ||
| 020 | |z 9780444517869 | ||
| 035 | |a (OCoLC)316566646 |z (OCoLC)646827534 |z (OCoLC)742295384 |z (OCoLC)816325397 |z (OCoLC)823122218 |z (OCoLC)823843629 |z (OCoLC)823912396 |z (OCoLC)824099400 |z (OCoLC)824154823 | ||
| 050 | 4 | |a QA431 |b .B87 1983eb | |
| 072 | 7 | |a MAT |x 007000 |2 bisacsh | |
| 082 | 7 | |a 515/.38 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Burton, T. A. |q (Theodore Allen), |d 1935- |1 https://id.oclc.org/worldcat/entity/E39PBJgCKyrdGtDMDhGwQ6RVG3 |0 http://id.loc.gov/authorities/names/n80092046 | |
| 245 | 1 | 0 | |a Volterra integral and differential equations / |c T.A. Burton. |
| 260 | |a New York : |b Academic Press, |c 1983. | ||
| 300 | |a 1 online resource (x, 313 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Mathematics in science and engineering ; |v v. 167 | |
| 504 | |a Includes bibliographical references (pages 303-307) and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Front Cover; Volterra Integral and Differential Equations; Copyright Page; Contents; Preface; Chapter 0. Introduction and Overview; 0.1. Statement of Purpose; 0.2. An Overview; Chapter 1. The General Problems; 1.1. Introduction; 1.2. Relations between Differential and Integral Equations; 1.3. A Glance at Initial Conditions and Existence; 1.4. Building the Intuition; 1.5. Reducible Equations; Chapter 2. Linear Equations; 2.1. Existence Theory; 2.2. Linear Properties; 2.3. Convolution and the Laplace Transform; 2.4. Stability; 2.5. Liapunov Functionals and Small Kernels | |
| 505 | 8 | |a 2.6. Uniform Asymptotic Stability2.7. Reducible Equations Revisited; 2.8. The Resolvent; Chapter 3. Existence Properties; 3.1. Definitions, Background, and Review; 3.2. Existence and Uniqueness; 3.3. Continuation of Solutions; 3.4. Continuity of Solutions; Chapter 4. History, Examples, and Motivation; 4.0. Introduction; 4.1. Volterra and Mathematical Biology; 4.2. Renewal Theory; 4.3. Examples; Chapter 5. Instability, Stability, and Perturbations; 5.1. The Matrix ATB + BA; 5.2. The Scalar Equation; 5.3. The Vector Equation; 5.4. Complete Instability; Chapter 6. Stability and Boundedness | |
| 505 | 8 | |a 6.1. Stability Theory for Ordinary Differential Equations6.2. Construction of Liapunov Functions; 6.3. A First Integral Liapunov Functional; 6.4. Nonlinear Considerations and an Annulus Argument; 6.5. A Functional in the Unstable Case; Chapter 7. Perturbations; 7.1. A Converse Theorem Yielding a Perturbation Result; 7.2. Boundedness under Perturbations; 7.3. Additive Properties of Functionals; Chapter 8. Functional Differential Equations; 8.0. Introduction; 8.1. Existence and Uniqueness; 8.2. Asymptotic Stability; 8.3. Equations with Bounded Delay; 8.4. Boundedness with Unbounded Delay | |
| 505 | 8 | |a 8.5. Limit Sets8.6. Periodic Solutions; 8.7. Limit Sets and Unbounded Delays; References; Author Index; Subject Index | |
| 520 | |a Volterra integral and differential equations. | ||
| 650 | 0 | |a Volterra equations. |0 http://id.loc.gov/authorities/subjects/sh85144322 | |
| 650 | 0 | |a Integro-differential equations. |0 http://id.loc.gov/authorities/subjects/sh85067135 | |
| 650 | 6 | |a Équations de Volterra. | |
| 650 | 6 | |a Équations intégrodifférentielles. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Integro-differential equations |2 fast | |
| 650 | 7 | |a Volterra equations |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Burton, T.A. (Theodore Allen), 1935- |t Volterra integral and differential equations. |d New York : Academic Press, 1983 |z 9780121473808 |w (OCoLC)316566646 |
| 830 | 0 | |a Mathematics in science and engineering ; |v v. 167. |0 http://id.loc.gov/authorities/names/n42015986 | |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297013 |3 Volltext |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://www.sciencedirect.com/science/bookseries/00765392/167 |3 Volltext |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL452956 | ||
| 938 | |a ebrary |b EBRY |n ebr10329445 | ||
| 938 | |a EBSCOhost |b EBSC |n 297013 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n 229048 | ||
| 938 | |a Internet Archive |b INAR |n volterraintegral0000burt | ||
| 938 | |a YBP Library Services |b YANK |n 3101867 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn316566646 |
|---|---|
| _version_ | 1816881689323896832 |
| adam_text | |
| any_adam_object | |
| author | Burton, T. A. (Theodore Allen), 1935- |
| author_GND | http://id.loc.gov/authorities/names/n80092046 |
| author_facet | Burton, T. A. (Theodore Allen), 1935- |
| author_role | |
| author_sort | Burton, T. A. 1935- |
| author_variant | t a b ta tab |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA431 |
| callnumber-raw | QA431 .B87 1983eb |
| callnumber-search | QA431 .B87 1983eb |
| callnumber-sort | QA 3431 B87 41983EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Front Cover; Volterra Integral and Differential Equations; Copyright Page; Contents; Preface; Chapter 0. Introduction and Overview; 0.1. Statement of Purpose; 0.2. An Overview; Chapter 1. The General Problems; 1.1. Introduction; 1.2. Relations between Differential and Integral Equations; 1.3. A Glance at Initial Conditions and Existence; 1.4. Building the Intuition; 1.5. Reducible Equations; Chapter 2. Linear Equations; 2.1. Existence Theory; 2.2. Linear Properties; 2.3. Convolution and the Laplace Transform; 2.4. Stability; 2.5. Liapunov Functionals and Small Kernels 2.6. Uniform Asymptotic Stability2.7. Reducible Equations Revisited; 2.8. The Resolvent; Chapter 3. Existence Properties; 3.1. Definitions, Background, and Review; 3.2. Existence and Uniqueness; 3.3. Continuation of Solutions; 3.4. Continuity of Solutions; Chapter 4. History, Examples, and Motivation; 4.0. Introduction; 4.1. Volterra and Mathematical Biology; 4.2. Renewal Theory; 4.3. Examples; Chapter 5. Instability, Stability, and Perturbations; 5.1. The Matrix ATB + BA; 5.2. The Scalar Equation; 5.3. The Vector Equation; 5.4. Complete Instability; Chapter 6. Stability and Boundedness 6.1. Stability Theory for Ordinary Differential Equations6.2. Construction of Liapunov Functions; 6.3. A First Integral Liapunov Functional; 6.4. Nonlinear Considerations and an Annulus Argument; 6.5. A Functional in the Unstable Case; Chapter 7. Perturbations; 7.1. A Converse Theorem Yielding a Perturbation Result; 7.2. Boundedness under Perturbations; 7.3. Additive Properties of Functionals; Chapter 8. Functional Differential Equations; 8.0. Introduction; 8.1. Existence and Uniqueness; 8.2. Asymptotic Stability; 8.3. Equations with Bounded Delay; 8.4. Boundedness with Unbounded Delay 8.5. Limit Sets8.6. Periodic Solutions; 8.7. Limit Sets and Unbounded Delays; References; Author Index; Subject Index |
| ctrlnum | (OCoLC)316566646 |
| dewey-full | 515/.38 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.38 |
| dewey-search | 515/.38 |
| dewey-sort | 3515 238 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04983cam a2200637 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn316566646</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">090320s1983 nyu ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">OPELS</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">OPELS</subfield><subfield code="d">N$T</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">EBLCP</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OPELS</subfield><subfield code="d">E7B</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OPELS</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UIU</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">DEBBG</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">NLGGC</subfield><subfield code="d">UIU</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">STF</subfield><subfield code="d">LEAUB</subfield><subfield code="d">M8D</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">SGP</subfield><subfield code="d">INARC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">646827534</subfield><subfield code="a">742295384</subfield><subfield code="a">816325397</subfield><subfield code="a">823122218</subfield><subfield code="a">823843629</subfield><subfield code="a">823912396</subfield><subfield code="a">824099400</subfield><subfield code="a">824154823</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780080956732</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0080956734</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9780121473808</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">0121473805</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9780444517869</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)316566646</subfield><subfield code="z">(OCoLC)646827534</subfield><subfield code="z">(OCoLC)742295384</subfield><subfield code="z">(OCoLC)816325397</subfield><subfield code="z">(OCoLC)823122218</subfield><subfield code="z">(OCoLC)823843629</subfield><subfield code="z">(OCoLC)823912396</subfield><subfield code="z">(OCoLC)824099400</subfield><subfield code="z">(OCoLC)824154823</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA431</subfield><subfield code="b">.B87 1983eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">007000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515/.38</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Burton, T. A.</subfield><subfield code="q">(Theodore Allen),</subfield><subfield code="d">1935-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJgCKyrdGtDMDhGwQ6RVG3</subfield><subfield code="0">http://id.loc.gov/authorities/names/n80092046</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Volterra integral and differential equations /</subfield><subfield code="c">T.A. Burton.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">New York :</subfield><subfield code="b">Academic Press,</subfield><subfield code="c">1983.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (x, 313 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematics in science and engineering ;</subfield><subfield code="v">v. 167</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 303-307) and indexes.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Front Cover; Volterra Integral and Differential Equations; Copyright Page; Contents; Preface; Chapter 0. Introduction and Overview; 0.1. Statement of Purpose; 0.2. An Overview; Chapter 1. The General Problems; 1.1. Introduction; 1.2. Relations between Differential and Integral Equations; 1.3. A Glance at Initial Conditions and Existence; 1.4. Building the Intuition; 1.5. Reducible Equations; Chapter 2. Linear Equations; 2.1. Existence Theory; 2.2. Linear Properties; 2.3. Convolution and the Laplace Transform; 2.4. Stability; 2.5. Liapunov Functionals and Small Kernels</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.6. Uniform Asymptotic Stability2.7. Reducible Equations Revisited; 2.8. The Resolvent; Chapter 3. Existence Properties; 3.1. Definitions, Background, and Review; 3.2. Existence and Uniqueness; 3.3. Continuation of Solutions; 3.4. Continuity of Solutions; Chapter 4. History, Examples, and Motivation; 4.0. Introduction; 4.1. Volterra and Mathematical Biology; 4.2. Renewal Theory; 4.3. Examples; Chapter 5. Instability, Stability, and Perturbations; 5.1. The Matrix ATB + BA; 5.2. The Scalar Equation; 5.3. The Vector Equation; 5.4. Complete Instability; Chapter 6. Stability and Boundedness</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6.1. Stability Theory for Ordinary Differential Equations6.2. Construction of Liapunov Functions; 6.3. A First Integral Liapunov Functional; 6.4. Nonlinear Considerations and an Annulus Argument; 6.5. A Functional in the Unstable Case; Chapter 7. Perturbations; 7.1. A Converse Theorem Yielding a Perturbation Result; 7.2. Boundedness under Perturbations; 7.3. Additive Properties of Functionals; Chapter 8. Functional Differential Equations; 8.0. Introduction; 8.1. Existence and Uniqueness; 8.2. Asymptotic Stability; 8.3. Equations with Bounded Delay; 8.4. Boundedness with Unbounded Delay</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">8.5. Limit Sets8.6. Periodic Solutions; 8.7. Limit Sets and Unbounded Delays; References; Author Index; Subject Index</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Volterra integral and differential equations.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Volterra equations.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85144322</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Integro-differential equations.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85067135</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Équations de Volterra.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Équations intégrodifférentielles.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Differential Equations</subfield><subfield code="x">General.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Integro-differential equations</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Volterra equations</subfield><subfield code="2">fast</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Burton, T.A. (Theodore Allen), 1935-</subfield><subfield code="t">Volterra integral and differential equations.</subfield><subfield code="d">New York : Academic Press, 1983</subfield><subfield code="z">9780121473808</subfield><subfield code="w">(OCoLC)316566646</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematics in science and engineering ;</subfield><subfield code="v">v. 167.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n42015986</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297013</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://www.sciencedirect.com/science/bookseries/00765392/167</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest Ebook Central</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL452956</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10329445</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">297013</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">229048</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Internet Archive</subfield><subfield code="b">INAR</subfield><subfield code="n">volterraintegral0000burt</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">3101867</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn316566646 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:42Z |
| institution | BVB |
| isbn | 9780080956732 0080956734 |
| language | English |
| oclc_num | 316566646 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (x, 313 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Academic Press, |
| record_format | marc |
| series | Mathematics in science and engineering ; |
| series2 | Mathematics in science and engineering ; |
| spelling | Burton, T. A. (Theodore Allen), 1935- https://id.oclc.org/worldcat/entity/E39PBJgCKyrdGtDMDhGwQ6RVG3 http://id.loc.gov/authorities/names/n80092046 Volterra integral and differential equations / T.A. Burton. New York : Academic Press, 1983. 1 online resource (x, 313 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics in science and engineering ; v. 167 Includes bibliographical references (pages 303-307) and indexes. Print version record. Front Cover; Volterra Integral and Differential Equations; Copyright Page; Contents; Preface; Chapter 0. Introduction and Overview; 0.1. Statement of Purpose; 0.2. An Overview; Chapter 1. The General Problems; 1.1. Introduction; 1.2. Relations between Differential and Integral Equations; 1.3. A Glance at Initial Conditions and Existence; 1.4. Building the Intuition; 1.5. Reducible Equations; Chapter 2. Linear Equations; 2.1. Existence Theory; 2.2. Linear Properties; 2.3. Convolution and the Laplace Transform; 2.4. Stability; 2.5. Liapunov Functionals and Small Kernels 2.6. Uniform Asymptotic Stability2.7. Reducible Equations Revisited; 2.8. The Resolvent; Chapter 3. Existence Properties; 3.1. Definitions, Background, and Review; 3.2. Existence and Uniqueness; 3.3. Continuation of Solutions; 3.4. Continuity of Solutions; Chapter 4. History, Examples, and Motivation; 4.0. Introduction; 4.1. Volterra and Mathematical Biology; 4.2. Renewal Theory; 4.3. Examples; Chapter 5. Instability, Stability, and Perturbations; 5.1. The Matrix ATB + BA; 5.2. The Scalar Equation; 5.3. The Vector Equation; 5.4. Complete Instability; Chapter 6. Stability and Boundedness 6.1. Stability Theory for Ordinary Differential Equations6.2. Construction of Liapunov Functions; 6.3. A First Integral Liapunov Functional; 6.4. Nonlinear Considerations and an Annulus Argument; 6.5. A Functional in the Unstable Case; Chapter 7. Perturbations; 7.1. A Converse Theorem Yielding a Perturbation Result; 7.2. Boundedness under Perturbations; 7.3. Additive Properties of Functionals; Chapter 8. Functional Differential Equations; 8.0. Introduction; 8.1. Existence and Uniqueness; 8.2. Asymptotic Stability; 8.3. Equations with Bounded Delay; 8.4. Boundedness with Unbounded Delay 8.5. Limit Sets8.6. Periodic Solutions; 8.7. Limit Sets and Unbounded Delays; References; Author Index; Subject Index Volterra integral and differential equations. Volterra equations. http://id.loc.gov/authorities/subjects/sh85144322 Integro-differential equations. http://id.loc.gov/authorities/subjects/sh85067135 Équations de Volterra. Équations intégrodifférentielles. MATHEMATICS Differential Equations General. bisacsh Integro-differential equations fast Volterra equations fast Print version: Burton, T.A. (Theodore Allen), 1935- Volterra integral and differential equations. New York : Academic Press, 1983 9780121473808 (OCoLC)316566646 Mathematics in science and engineering ; v. 167. http://id.loc.gov/authorities/names/n42015986 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297013 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://www.sciencedirect.com/science/bookseries/00765392/167 Volltext |
| spellingShingle | Burton, T. A. (Theodore Allen), 1935- Volterra integral and differential equations / Mathematics in science and engineering ; Front Cover; Volterra Integral and Differential Equations; Copyright Page; Contents; Preface; Chapter 0. Introduction and Overview; 0.1. Statement of Purpose; 0.2. An Overview; Chapter 1. The General Problems; 1.1. Introduction; 1.2. Relations between Differential and Integral Equations; 1.3. A Glance at Initial Conditions and Existence; 1.4. Building the Intuition; 1.5. Reducible Equations; Chapter 2. Linear Equations; 2.1. Existence Theory; 2.2. Linear Properties; 2.3. Convolution and the Laplace Transform; 2.4. Stability; 2.5. Liapunov Functionals and Small Kernels 2.6. Uniform Asymptotic Stability2.7. Reducible Equations Revisited; 2.8. The Resolvent; Chapter 3. Existence Properties; 3.1. Definitions, Background, and Review; 3.2. Existence and Uniqueness; 3.3. Continuation of Solutions; 3.4. Continuity of Solutions; Chapter 4. History, Examples, and Motivation; 4.0. Introduction; 4.1. Volterra and Mathematical Biology; 4.2. Renewal Theory; 4.3. Examples; Chapter 5. Instability, Stability, and Perturbations; 5.1. The Matrix ATB + BA; 5.2. The Scalar Equation; 5.3. The Vector Equation; 5.4. Complete Instability; Chapter 6. Stability and Boundedness 6.1. Stability Theory for Ordinary Differential Equations6.2. Construction of Liapunov Functions; 6.3. A First Integral Liapunov Functional; 6.4. Nonlinear Considerations and an Annulus Argument; 6.5. A Functional in the Unstable Case; Chapter 7. Perturbations; 7.1. A Converse Theorem Yielding a Perturbation Result; 7.2. Boundedness under Perturbations; 7.3. Additive Properties of Functionals; Chapter 8. Functional Differential Equations; 8.0. Introduction; 8.1. Existence and Uniqueness; 8.2. Asymptotic Stability; 8.3. Equations with Bounded Delay; 8.4. Boundedness with Unbounded Delay 8.5. Limit Sets8.6. Periodic Solutions; 8.7. Limit Sets and Unbounded Delays; References; Author Index; Subject Index Volterra equations. http://id.loc.gov/authorities/subjects/sh85144322 Integro-differential equations. http://id.loc.gov/authorities/subjects/sh85067135 Équations de Volterra. Équations intégrodifférentielles. MATHEMATICS Differential Equations General. bisacsh Integro-differential equations fast Volterra equations fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85144322 http://id.loc.gov/authorities/subjects/sh85067135 |
| title | Volterra integral and differential equations / |
| title_auth | Volterra integral and differential equations / |
| title_exact_search | Volterra integral and differential equations / |
| title_full | Volterra integral and differential equations / T.A. Burton. |
| title_fullStr | Volterra integral and differential equations / T.A. Burton. |
| title_full_unstemmed | Volterra integral and differential equations / T.A. Burton. |
| title_short | Volterra integral and differential equations / |
| title_sort | volterra integral and differential equations |
| topic | Volterra equations. http://id.loc.gov/authorities/subjects/sh85144322 Integro-differential equations. http://id.loc.gov/authorities/subjects/sh85067135 Équations de Volterra. Équations intégrodifférentielles. MATHEMATICS Differential Equations General. bisacsh Integro-differential equations fast Volterra equations fast |
| topic_facet | Volterra equations. Integro-differential equations. Équations de Volterra. Équations intégrodifférentielles. MATHEMATICS Differential Equations General. Integro-differential equations Volterra equations |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297013 https://www.sciencedirect.com/science/bookseries/00765392/167 |
| work_keys_str_mv | AT burtonta volterraintegralanddifferentialequations |