A history of the calculus of variations from the 17th through the 19th century:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1980
|
| Series: | Studies in the history of mathematics and physical sciences
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 410 S. graph. Darst. |
| ISBN: | 0387905219 3540905219 |
Staff View
MARC
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| 100 | 1 | |a Goldstine, Herman H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A history of the calculus of variations from the 17th through the 19th century |c Herman H. Goldstine |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1980 | |
| 300 | |a XVIII, 410 S. |b graph. Darst. | ||
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| 650 | 4 | |a Calcul des variations - Histoire | |
| 650 | 7 | |a Calcul des variations - Histoire |2 ram | |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Introduction xiii
1. Fermat, Newton, Leibniz, and the
Bernoullis l
1.1. Fermat s Principle of Least Time 1
1.2. Newton s Problem of Motion in a Resisting Medium 07
1.3. The Brachystochrone Problem 30
1.4. The Problem Itself 32
1.5. Newton s Solution of the Brachystochrone Problem 34
1.6. Leibniz s Solution of the Brachystochrone Problem 35
1.7. John Bernoulli s First Published Solution and Some
Related Work 38
1.8. James Bernoulli s Solution 44
1.9. James Bernoulli s Challenge to His Brother 47
1.10. James Bernoulli s Method 50
1.11. John Bernoulli s 1718 Paper 58
2. Euler 67
2.1. Introduction 67
2.2. The Simplest Problems 68
2.3. More General Problems 73
2.4. Invariance Questions 84
2.5. Isoperimetric Problems 92
2.6. Isoperimetric Problems, Continuation 99
2.7. The Principle of Least Action 101
2.8. Maupertuis on Least Action 108
3. Lagrange and Legendre 110
3.1. Lagrange s First Letter to Euler 110
3.2. Lagrange s First Paper 115
3.3. Lagrange s Second Paper 129
3.4. Legendre s Analysis of the Second Variation 139
3.5. Excursus 145
3.6. The Euler Lagrange Multiplier Rule 148
ix
x Table of Contents
4. Jacobi and His School 151
4.1. Excursus 151
4.2. Jacobi s Paper of 1836 156
4.3. Excursus on Planetary Motion 164
4.4. V. A. Lebesgue s Proof 168
4.5. Hamilton Jacobi Theory 176
4.6. Hesse s Commentary 186
5. Weierstrass 190
5.1. Weierstrass s Lectures 190
5.2. The Formulation of the Parametric Problem 191
5.3. The Second Variation 193
5.4. Conjugate Points 197
5.5. Necessary Conditions and Sufficient Conditions 201
5.6. Geometrical Considerations of Conjugate Points 204
5.7. The Weierstrass Condition 210
5.8. Sufficiency Arguments 214
5.9. The Isoperimetric Problem 219
5.10. Sufficient Conditions 223
5.11. Scheeffer s Results 237
5.12. Schwarz s Proof of the Jacobi Condition 245
5.13. Osgood s Summary 246
6. Clebsch, Mayer, and Others 250
6.1. Introduction 250
6.2. Clebsch s Treatment of the Second Variation 250
6.3. Clebsch, Continuation 257
6.4. Mayer s Contributions 269
6.5. Lagrange s Multiplier Rule 282
6.6. Excursus on the Fundamental Lemma and on
Isoperimetric Problems 287
6.7. The Problem of Mayer 300
7. Hilbert, Kneser, and Others 314
7.1. Hilbert s Invariant Integral 314
7.2. Existence of a Field 317
7.3. Hibert, Continuation 322
7.4. Mayer Families of Extremals 330
7.5. Kneser s Methods 338
7.6. Kneser on Focal Points and Transversality 346
7.7. Bliss s Work on Problems in Three Space 357
7.8. Boundary Value Methods 362
7.9. Hilbert s Existence Theorem 371
Table of Contents xi
7.10. Bolza and the Problem of Bolza 373
7.11. Caratheodory s Method 383
7.12. Hahn on Abnormality 387
Bibliography 391
Index 40i
|
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| author | Goldstine, Herman H. |
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| dewey-full | 515/.64/0903 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.64/0903 |
| dewey-search | 515/.64/0903 |
| dewey-sort | 3515 264 3903 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| era | Geschichte 1600-1900 gnd |
| era_facet | Geschichte 1600-1900 |
| format | Book |
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| id | DE-604.BV008578568 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:21:22Z |
| institution | BVB |
| isbn | 0387905219 3540905219 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005638037 |
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| physical | XVIII, 410 S. graph. Darst. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Springer |
| record_format | marc |
| series | Studies in the history of mathematics and physical sciences |
| series2 | Studies in the history of mathematics and physical sciences |
| spelling | Goldstine, Herman H. Verfasser aut A history of the calculus of variations from the 17th through the 19th century Herman H. Goldstine New York [u.a.] Springer 1980 XVIII, 410 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in the history of mathematics and physical sciences 5 Geschichte 1600-1900 gnd rswk-swf Calcul des variations - Histoire Calcul des variations - Histoire ram Variatierekening gtt Geschichte Calculus of variations History Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Geschichte 1600-1900 z DE-604 Studies in the history of mathematics and physical sciences 5 (DE-604)BV000003995 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005638037&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goldstine, Herman H. A history of the calculus of variations from the 17th through the 19th century Studies in the history of mathematics and physical sciences Calcul des variations - Histoire Calcul des variations - Histoire ram Variatierekening gtt Geschichte Calculus of variations History Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4062355-5 |
| title | A history of the calculus of variations from the 17th through the 19th century |
| title_auth | A history of the calculus of variations from the 17th through the 19th century |
| title_exact_search | A history of the calculus of variations from the 17th through the 19th century |
| title_full | A history of the calculus of variations from the 17th through the 19th century Herman H. Goldstine |
| title_fullStr | A history of the calculus of variations from the 17th through the 19th century Herman H. Goldstine |
| title_full_unstemmed | A history of the calculus of variations from the 17th through the 19th century Herman H. Goldstine |
| title_short | A history of the calculus of variations from the 17th through the 19th century |
| title_sort | a history of the calculus of variations from the 17th through the 19th century |
| topic | Calcul des variations - Histoire Calcul des variations - Histoire ram Variatierekening gtt Geschichte Calculus of variations History Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Calcul des variations - Histoire Variatierekening Geschichte Calculus of variations History Variationsrechnung |
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