Exterior Differential Systems and the Calculus of Variations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
1983
|
| Series: | Progress in Mathematics
25 |
| Subjects: | |
| Links: | https://doi.org/10.1007/978-1-4615-8166-6 |
| Item Description: | 15 0. PRELIMINARIES a) Notations from Manifold Theory b) The Language of Jet Manifolds c) Frame Manifolds d) Differentia! Ideals e) Exterior Differential Systems EULER-LAGRANGE EQUATIONS FOR DIFFERENTIAL SYSTEMS ~liTH ONE I. 32 INDEPENDENT VARIABLE a) Setting up the Problem; Classical Examples b) Variational Equations for Integral Manifolds of Differential Systems c) Differential Systems in Good Form; the Derived Flag, Cauchy Characteristics, and Prolongation of Exterior Differential Systems d) Derivation of the Euler-Lagrange Equations; Examples e) The Euler-Lagrange Differential System; Non-Degenerate Variational Problems; Examples FIRST INTEGRALS OF THE EULER-LAGRANGE SYSTEM; NOETHER'S II. 1D7 THEOREM AND EXAMPLES a) First Integrals and Noether's Theorem; Some Classical Examples; Variational Problems Algebraically Integrable by Quadratures b) Investigation of the Euler-Lagrange System for Some Differential-Geometric Variational Pro~lems: 2 i) ( K ds for Plane Curves; i i) Affine Arclength; 2 iii) f K ds for Space Curves; and iv) Delauney Problem. II I. EULER EQUATIONS FOR VARIATIONAL PROBLEfiJS IN HOMOGENEOUS SPACES 161 a) Derivation of the Equations: i) Motivation; i i) Review of the Classical Case; iii) the Genera 1 Euler Equations 2 K /2 ds b) Examples: i) the Euler Equations Associated to f for lEn; but for Curves in i i) Some Problems as in i) sn; Non- Curves in iii) Euler Equations Associated to degenerate Ruled Surfaces IV. |
| Physical Description: | 1 Online-Ressource (IX, 339 p) |
| ISBN: | 9781461581666 9780817631031 |
| DOI: | 10.1007/978-1-4615-8166-6 |
Staff View
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042420959 | ||
| 003 | DE-604 | ||
| 005 | 20210514 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1983 xx o|||| 00||| eng d | ||
| 020 | |a 9781461581666 |c Online |9 978-1-4615-8166-6 | ||
| 020 | |a 9780817631031 |c Print |9 978-0-8176-3103-1 | ||
| 024 | 7 | |a 10.1007/978-1-4615-8166-6 |2 doi | |
| 035 | |a (OCoLC)879624749 | ||
| 035 | |a (DE-599)BVBBV042420959 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.64 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Griffiths, Phillip |d 1938- |e Verfasser |0 (DE-588)131881434 |4 aut | |
| 245 | 1 | 0 | |a Exterior Differential Systems and the Calculus of Variations |c by Phillip A. Griffiths |
| 264 | 1 | |a Boston, MA |b Birkhäuser Boston |c 1983 | |
| 300 | |a 1 Online-Ressource (IX, 339 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Progress in Mathematics |v 25 | |
| 500 | |a 15 0. PRELIMINARIES a) Notations from Manifold Theory b) The Language of Jet Manifolds c) Frame Manifolds d) Differentia! Ideals e) Exterior Differential Systems EULER-LAGRANGE EQUATIONS FOR DIFFERENTIAL SYSTEMS ~liTH ONE I. 32 INDEPENDENT VARIABLE a) Setting up the Problem; Classical Examples b) Variational Equations for Integral Manifolds of Differential Systems c) Differential Systems in Good Form; the Derived Flag, Cauchy Characteristics, and Prolongation of Exterior Differential Systems d) Derivation of the Euler-Lagrange Equations; Examples e) The Euler-Lagrange Differential System; Non-Degenerate Variational Problems; Examples FIRST INTEGRALS OF THE EULER-LAGRANGE SYSTEM; NOETHER'S II. 1D7 THEOREM AND EXAMPLES a) First Integrals and Noether's Theorem; Some Classical Examples; Variational Problems Algebraically Integrable by Quadratures b) Investigation of the Euler-Lagrange System for Some Differential-Geometric Variational Pro~lems: 2 i) ( K ds for Plane Curves; i i) Affine Arclength; 2 iii) f K ds for Space Curves; and iv) Delauney Problem. II I. EULER EQUATIONS FOR VARIATIONAL PROBLEfiJS IN HOMOGENEOUS SPACES 161 a) Derivation of the Equations: i) Motivation; i i) Review of the Classical Case; iii) the Genera 1 Euler Equations 2 K /2 ds b) Examples: i) the Euler Equations Associated to f for lEn; but for Curves in i i) Some Problems as in i) sn; Non- Curves in iii) Euler Equations Associated to degenerate Ruled Surfaces IV. | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Calculus of Variations and Optimal Control; Optimization | |
| 650 | 4 | |a Dynamical Systems and Ergodic Theory | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Variationsrechnung |0 (DE-588)4062355-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Äußeres Differentialsystem |0 (DE-588)4141545-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Variationsrechnung |0 (DE-588)4062355-5 |D s |
| 689 | 0 | 1 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Variationsrechnung |0 (DE-588)4062355-5 |D s |
| 689 | 1 | 1 | |a Äußeres Differentialsystem |0 (DE-588)4141545-0 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-0-8176-3103-1 |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4615-8166-6 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027856376 | |
Record in the Search Index
| DE-BY-TUM_katkey | 2067968 |
|---|---|
| _version_ | 1821931205469143040 |
| any_adam_object | |
| author | Griffiths, Phillip 1938- |
| author_GND | (DE-588)131881434 |
| author_facet | Griffiths, Phillip 1938- |
| author_role | aut |
| author_sort | Griffiths, Phillip 1938- |
| author_variant | p g pg |
| building | Verbundindex |
| bvnumber | BV042420959 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879624749 (DE-599)BVBBV042420959 |
| dewey-full | 515.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.64 |
| dewey-search | 515.64 |
| dewey-sort | 3515.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4615-8166-6 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03699nam a2200589zcb4500</leader><controlfield tag="001">BV042420959</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210514 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1983 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461581666</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4615-8166-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780817631031</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-8176-3103-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4615-8166-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)879624749</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042420959</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.64</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Griffiths, Phillip</subfield><subfield code="d">1938-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)131881434</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Exterior Differential Systems and the Calculus of Variations</subfield><subfield code="c">by Phillip A. Griffiths</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston, MA</subfield><subfield code="b">Birkhäuser Boston</subfield><subfield code="c">1983</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (IX, 339 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Progress in Mathematics</subfield><subfield code="v">25</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">15 0. PRELIMINARIES a) Notations from Manifold Theory b) The Language of Jet Manifolds c) Frame Manifolds d) Differentia! Ideals e) Exterior Differential Systems EULER-LAGRANGE EQUATIONS FOR DIFFERENTIAL SYSTEMS ~liTH ONE I. 32 INDEPENDENT VARIABLE a) Setting up the Problem; Classical Examples b) Variational Equations for Integral Manifolds of Differential Systems c) Differential Systems in Good Form; the Derived Flag, Cauchy Characteristics, and Prolongation of Exterior Differential Systems d) Derivation of the Euler-Lagrange Equations; Examples e) The Euler-Lagrange Differential System; Non-Degenerate Variational Problems; Examples FIRST INTEGRALS OF THE EULER-LAGRANGE SYSTEM; NOETHER'S II. 1D7 THEOREM AND EXAMPLES a) First Integrals and Noether's Theorem; Some Classical Examples; Variational Problems Algebraically Integrable by Quadratures b) Investigation of the Euler-Lagrange System for Some Differential-Geometric Variational Pro~lems: 2 i) ( K ds for Plane Curves; i i) Affine Arclength; 2 iii) f K ds for Space Curves; and iv) Delauney Problem. II I. EULER EQUATIONS FOR VARIATIONAL PROBLEfiJS IN HOMOGENEOUS SPACES 161 a) Derivation of the Equations: i) Motivation; i i) Review of the Classical Case; iii) the Genera 1 Euler Equations 2 K /2 ds b) Examples: i) the Euler Equations Associated to f for lEn; but for Curves in i i) Some Problems as in i) sn; Non- Curves in iii) Euler Equations Associated to degenerate Ruled Surfaces IV.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differentiable dynamical systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Calculus of Variations and Optimal Control; Optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dynamical Systems and Ergodic Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Variationsrechnung</subfield><subfield code="0">(DE-588)4062355-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Äußeres Differentialsystem</subfield><subfield code="0">(DE-588)4141545-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Variationsrechnung</subfield><subfield code="0">(DE-588)4062355-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Variationsrechnung</subfield><subfield code="0">(DE-588)4062355-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Äußeres Differentialsystem</subfield><subfield code="0">(DE-588)4141545-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-0-8176-3103-1</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4615-8166-6</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027856376</subfield></datafield></record></collection> |
| id | DE-604.BV042420959 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:43Z |
| institution | BVB |
| isbn | 9781461581666 9780817631031 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856376 |
| oclc_num | 879624749 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (IX, 339 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Birkhäuser Boston |
| record_format | marc |
| series2 | Progress in Mathematics |
| spellingShingle | Griffiths, Phillip 1938- Exterior Differential Systems and the Calculus of Variations Mathematics Differentiable dynamical systems Mathematical optimization Calculus of Variations and Optimal Control; Optimization Dynamical Systems and Ergodic Theory Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Variationsrechnung (DE-588)4062355-5 gnd Äußeres Differentialsystem (DE-588)4141545-0 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4062355-5 (DE-588)4141545-0 |
| title | Exterior Differential Systems and the Calculus of Variations |
| title_auth | Exterior Differential Systems and the Calculus of Variations |
| title_exact_search | Exterior Differential Systems and the Calculus of Variations |
| title_full | Exterior Differential Systems and the Calculus of Variations by Phillip A. Griffiths |
| title_fullStr | Exterior Differential Systems and the Calculus of Variations by Phillip A. Griffiths |
| title_full_unstemmed | Exterior Differential Systems and the Calculus of Variations by Phillip A. Griffiths |
| title_short | Exterior Differential Systems and the Calculus of Variations |
| title_sort | exterior differential systems and the calculus of variations |
| topic | Mathematics Differentiable dynamical systems Mathematical optimization Calculus of Variations and Optimal Control; Optimization Dynamical Systems and Ergodic Theory Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Variationsrechnung (DE-588)4062355-5 gnd Äußeres Differentialsystem (DE-588)4141545-0 gnd |
| topic_facet | Mathematics Differentiable dynamical systems Mathematical optimization Calculus of Variations and Optimal Control; Optimization Dynamical Systems and Ergodic Theory Mathematik Differentialgeometrie Variationsrechnung Äußeres Differentialsystem |
| url | https://doi.org/10.1007/978-1-4615-8166-6 |
| work_keys_str_mv | AT griffithsphillip exteriordifferentialsystemsandthecalculusofvariations |