Partial Differential Equations II: Qualitative Studies of Linear Equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1996
|
| Schriftenreihe: | Applied Mathematical Sciences
116 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Partial differential equations is a many-faceted subject. Created to describe the mechanical behavior of objects such as vibrating strings and blowing winds, it has developed into a body of material that interacts with many branches of mathematics, such as differential geometry, complex analysis, and harmonic analysis, as well as a ubiquitous factor in the description and elucidation of problems in mathematical physics. This work is intended to provide a course of study of some of the major aspects of PDE. It is addressed to readers with a background in the basic introductory graduate mathematics courses in American universities: elementary real and complex analysis, differential geometry, and measure theory. Chapter 1 provides background material on the theory of ordinary differential equations (ODE). This includes both very basic material- on topics such as the existence and uniqueness of solutions to ODE and explicit solutions to equations with constant coefficients and relations to linear algebra- and more sophisticated results- on flows generated by vector fields, connections with differential geometry, the calculus of differential forms, stationary action principles in mechanics, and their relation to Hamiltonian systems. We discuss equations of relativistic motion as well as equations of classical Newtonian mechanics. There are also applications to topological results, such as degree theory, the Brouwer fixed-point theorem, and the Jordan-Brouwer separation theorem. In this chapter we also treat scalar first-order PDE, via Hamilton-Jacobi theory |
| Beschreibung: | 1 Online-Ressource (XXI, 529 p) |
| ISBN: | 9781475741872 9781475741896 |
| DOI: | 10.1007/978-1-4757-4187-2 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042421586 | ||
| 003 | DE-604 | ||
| 005 | 20200707 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1996 |||| o||u| ||||||eng d | ||
| 020 | |a 9781475741872 |c Online |9 978-1-4757-4187-2 | ||
| 020 | |a 9781475741896 |c Print |9 978-1-4757-4189-6 | ||
| 024 | 7 | |a 10.1007/978-1-4757-4187-2 |2 doi | |
| 035 | |a (OCoLC)864046252 | ||
| 035 | |a (DE-599)BVBBV042421586 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Taylor, Michael Eugene |d 1946- |e Verfasser |0 (DE-588)123980119 |4 aut | |
| 245 | 1 | 0 | |a Partial Differential Equations II |b Qualitative Studies of Linear Equations |c by Michael E. Taylor |
| 264 | 1 | |a New York, NY |b Springer New York |c 1996 | |
| 300 | |a 1 Online-Ressource (XXI, 529 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Applied Mathematical Sciences |v 116 | |
| 500 | |a Partial differential equations is a many-faceted subject. Created to describe the mechanical behavior of objects such as vibrating strings and blowing winds, it has developed into a body of material that interacts with many branches of mathematics, such as differential geometry, complex analysis, and harmonic analysis, as well as a ubiquitous factor in the description and elucidation of problems in mathematical physics. This work is intended to provide a course of study of some of the major aspects of PDE. It is addressed to readers with a background in the basic introductory graduate mathematics courses in American universities: elementary real and complex analysis, differential geometry, and measure theory. Chapter 1 provides background material on the theory of ordinary differential equations (ODE). This includes both very basic material- on topics such as the existence and uniqueness of solutions to ODE and explicit solutions to equations with constant coefficients and relations to linear algebra- and more sophisticated results- on flows generated by vector fields, connections with differential geometry, the calculus of differential forms, stationary action principles in mechanics, and their relation to Hamiltonian systems. We discuss equations of relativistic motion as well as equations of classical Newtonian mechanics. There are also applications to topological results, such as degree theory, the Brouwer fixed-point theorem, and the Jordan-Brouwer separation theorem. In this chapter we also treat scalar first-order PDE, via Hamilton-Jacobi theory | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Analysis | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
| 650 | 4 | |a Theoretical, Mathematical and Computational Physics | |
| 650 | 4 | |a Mathematik | |
| 830 | 0 | |a Applied Mathematical Sciences |v 116 |w (DE-604)BV040244599 |9 116 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4757-4187-2 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027857003 | ||
Datensatz im Suchindex
| _version_ | 1804153094817185792 |
|---|---|
| any_adam_object | |
| author | Taylor, Michael Eugene 1946- |
| author_GND | (DE-588)123980119 |
| author_facet | Taylor, Michael Eugene 1946- |
| author_role | aut |
| author_sort | Taylor, Michael Eugene 1946- |
| author_variant | m e t me met |
| building | Verbundindex |
| bvnumber | BV042421586 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)864046252 (DE-599)BVBBV042421586 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-4187-2 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03178nmm a2200457zcb4500</leader><controlfield tag="001">BV042421586</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200707 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1996 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781475741872</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4757-4187-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781475741896</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4757-4189-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4757-4187-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)864046252</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421586</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</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</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">Taylor, Michael Eugene</subfield><subfield code="d">1946-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)123980119</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Partial Differential Equations II</subfield><subfield code="b">Qualitative Studies of Linear Equations</subfield><subfield code="c">by Michael E. Taylor</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XXI, 529 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="1" ind2=" "><subfield code="a">Applied Mathematical Sciences</subfield><subfield code="v">116</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Partial differential equations is a many-faceted subject. Created to describe the mechanical behavior of objects such as vibrating strings and blowing winds, it has developed into a body of material that interacts with many branches of mathematics, such as differential geometry, complex analysis, and harmonic analysis, as well as a ubiquitous factor in the description and elucidation of problems in mathematical physics. This work is intended to provide a course of study of some of the major aspects of PDE. It is addressed to readers with a background in the basic introductory graduate mathematics courses in American universities: elementary real and complex analysis, differential geometry, and measure theory. Chapter 1 provides background material on the theory of ordinary differential equations (ODE). This includes both very basic material- on topics such as the existence and uniqueness of solutions to ODE and explicit solutions to equations with constant coefficients and relations to linear algebra- and more sophisticated results- on flows generated by vector fields, connections with differential geometry, the calculus of differential forms, stationary action principles in mechanics, and their relation to Hamiltonian systems. We discuss equations of relativistic motion as well as equations of classical Newtonian mechanics. There are also applications to topological results, such as degree theory, the Brouwer fixed-point theorem, and the Jordan-Brouwer separation theorem. In this chapter we also treat scalar first-order PDE, via Hamilton-Jacobi theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global analysis (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distribution (Probability theory)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probability Theory and Stochastic Processes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Theoretical, Mathematical and Computational Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Applied Mathematical Sciences</subfield><subfield code="v">116</subfield><subfield code="w">(DE-604)BV040244599</subfield><subfield code="9">116</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4757-4187-2</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><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="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027857003</subfield></datafield></record></collection> |
| id | DE-604.BV042421586 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475741872 9781475741896 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857003 |
| oclc_num | 864046252 |
| 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 (XXI, 529 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer New York |
| record_format | marc |
| series | Applied Mathematical Sciences |
| series2 | Applied Mathematical Sciences |
| spelling | Taylor, Michael Eugene 1946- Verfasser (DE-588)123980119 aut Partial Differential Equations II Qualitative Studies of Linear Equations by Michael E. Taylor New York, NY Springer New York 1996 1 Online-Ressource (XXI, 529 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 116 Partial differential equations is a many-faceted subject. Created to describe the mechanical behavior of objects such as vibrating strings and blowing winds, it has developed into a body of material that interacts with many branches of mathematics, such as differential geometry, complex analysis, and harmonic analysis, as well as a ubiquitous factor in the description and elucidation of problems in mathematical physics. This work is intended to provide a course of study of some of the major aspects of PDE. It is addressed to readers with a background in the basic introductory graduate mathematics courses in American universities: elementary real and complex analysis, differential geometry, and measure theory. Chapter 1 provides background material on the theory of ordinary differential equations (ODE). This includes both very basic material- on topics such as the existence and uniqueness of solutions to ODE and explicit solutions to equations with constant coefficients and relations to linear algebra- and more sophisticated results- on flows generated by vector fields, connections with differential geometry, the calculus of differential forms, stationary action principles in mechanics, and their relation to Hamiltonian systems. We discuss equations of relativistic motion as well as equations of classical Newtonian mechanics. There are also applications to topological results, such as degree theory, the Brouwer fixed-point theorem, and the Jordan-Brouwer separation theorem. In this chapter we also treat scalar first-order PDE, via Hamilton-Jacobi theory Mathematics Global analysis (Mathematics) Distribution (Probability theory) Analysis Probability Theory and Stochastic Processes Theoretical, Mathematical and Computational Physics Mathematik Applied Mathematical Sciences 116 (DE-604)BV040244599 116 https://doi.org/10.1007/978-1-4757-4187-2 Verlag Volltext |
| spellingShingle | Taylor, Michael Eugene 1946- Partial Differential Equations II Qualitative Studies of Linear Equations Applied Mathematical Sciences Mathematics Global analysis (Mathematics) Distribution (Probability theory) Analysis Probability Theory and Stochastic Processes Theoretical, Mathematical and Computational Physics Mathematik |
| title | Partial Differential Equations II Qualitative Studies of Linear Equations |
| title_auth | Partial Differential Equations II Qualitative Studies of Linear Equations |
| title_exact_search | Partial Differential Equations II Qualitative Studies of Linear Equations |
| title_full | Partial Differential Equations II Qualitative Studies of Linear Equations by Michael E. Taylor |
| title_fullStr | Partial Differential Equations II Qualitative Studies of Linear Equations by Michael E. Taylor |
| title_full_unstemmed | Partial Differential Equations II Qualitative Studies of Linear Equations by Michael E. Taylor |
| title_short | Partial Differential Equations II |
| title_sort | partial differential equations ii qualitative studies of linear equations |
| title_sub | Qualitative Studies of Linear Equations |
| topic | Mathematics Global analysis (Mathematics) Distribution (Probability theory) Analysis Probability Theory and Stochastic Processes Theoretical, Mathematical and Computational Physics Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Distribution (Probability theory) Analysis Probability Theory and Stochastic Processes Theoretical, Mathematical and Computational Physics Mathematik |
| url | https://doi.org/10.1007/978-1-4757-4187-2 |
| volume_link | (DE-604)BV040244599 |
| work_keys_str_mv | AT taylormichaeleugene partialdifferentialequationsiiqualitativestudiesoflinearequations |