Lectures on partial differential equations of first order
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Notre Dame, Ind.
Univ. of Notre Dame Press
1972
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| 100 | 1 | |a Dou, Alberto |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lectures on partial differential equations of first order |c Alberto Dou |
| 264 | 1 | |a Notre Dame, Ind. |b Univ. of Notre Dame Press |c 1972 | |
| 300 | |a X, 171 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 4 | |a Differential equations, Partial | |
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Datensatz im Suchindex
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| _version_ | 1823051880006156288 |
| adam_text | SYSTEMATIC INDEX
Chapter I. QUASI LINEAR EQUATIONS 1
f 1. Introduction 1
1. The Standard Problem 1
2. Geometric Interpretation 2
3. Characteristic Curves 5
Exercises 7
§ 2. Integral Surfaces and First Integrals 11
1. The Jacob! Transformation 11
2. First Integrals of Characteristic Systems. 14
Exercises 20
§ 3. The Cauchy Problem 24
1. An Uniqueness Theorem 24
2. The Cauchy Problem in Two Dimensions 25
3. The Cauchy Problem in n Dimensions 31
4. Examples 32
Exercises 34
Chapter II. GENERAL EQUATION WITH TWO INDEPENDENT
VARIABLES 40
§ 4. Monge Curves 40
1. The Standard Conditions 40
2. Definitions and Geometric Interpretation . 41
3. Differential Systems of Monge Curves 43
f 5. The Cauchy Problem 49
1. The Standard Problem 49
2. Characteristic Strips 51
3. Uniqueness of the Solution of the Cauchy
Problem 55
4. Solution of the Cauchy Problem 58
5. Geometric Interpretation of Characteristic
Strips and Integral Surfaces 62
Exercises 65
ix
p 6. The Method of the Complete Integral 70
1. The Complete Integral 70
2. Total Differential Equations 78
3. Finding a Complete Integral 84
4. Kquation of the Monge Curves 86
5. Singular Integrals 89
Exercises 9^
f 7. Example: p2 + q2 + f(x,y) =0 101
1. Regularity of the Equation and its
Motivation 101
2. The Characteristic System and its Solution 103
3. Finding a Complete Integral 111
4. A Transverse Initial Strip. Transver
sality Condition. Initial Strips, Trans¬
versal or Singular 113
5. Integral Surfaces. Integral Conoids.
Wave Fronts, their Orthogonality with the
Characteristics 118
6. Connection with Fermat s Principle and
Calculus of Variations. Parallelism of
the Wave Fronts and Huyghens1 Construction 122
Exercises 127
Chapter III. EQUATIONS WITH MORE THAN TWO INDE¬
PENDENT VARIABLES 130
$ 8. The Cauchy Method 130
1. Characteristic System and Strips 130
2. The Cauchy Problem 135
3. The Singular Case, A = 0 138
Exercises 148
§ 9. Hamilton Jacobl Method 149
1. Characteristic System and Complete
Integrals 149
2. The Hamilton Jacob! Theorem 153
3. The Cauchy Problem 158
Exercises 160
Bibliographical Note 169
Analytical Index 170
x
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| any_adam_object | 1 |
| author | Dou, Alberto |
| author_facet | Dou, Alberto |
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002645944 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-03T16:44:36Z |
| institution | BVB |
| isbn | 0268004684 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001697763 |
| oclc_num | 363946 |
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| physical | X, 171 S. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
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| publisher | Univ. of Notre Dame Press |
| record_format | marc |
| spellingShingle | Dou, Alberto Lectures on partial differential equations of first order Équations aux dérivées partielles Differential equations, Partial |
| title | Lectures on partial differential equations of first order |
| title_auth | Lectures on partial differential equations of first order |
| title_exact_search | Lectures on partial differential equations of first order |
| title_full | Lectures on partial differential equations of first order Alberto Dou |
| title_fullStr | Lectures on partial differential equations of first order Alberto Dou |
| title_full_unstemmed | Lectures on partial differential equations of first order Alberto Dou |
| title_short | Lectures on partial differential equations of first order |
| title_sort | lectures on partial differential equations of first order |
| topic | Équations aux dérivées partielles Differential equations, Partial |
| topic_facet | Équations aux dérivées partielles Differential equations, Partial |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001697763&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT doualberto lecturesonpartialdifferentialequationsoffirstorder |