Theory of partial differential equations /:
Theory of partial differential equations.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Academic Press,
1972.
|
| Schriftenreihe: | Mathematics in science and engineering ;
v. 93. |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Zusammenfassung: | Theory of partial differential equations. |
| Beschreibung: | 1 online resource (xiv, 283 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 264-266) and index. |
| ISBN: | 9780124495500 0124495508 9780080956022 0080956025 1282290398 9781282290396 |
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| 245 | 1 | 0 | |a Theory of partial differential equations / |c H. Melvin Lieberstein. |
| 260 | |a New York : |b Academic Press, |c 1972. | ||
| 300 | |a 1 online resource (xiv, 283 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Mathematics in science and engineering ; |v v. 93 | |
| 504 | |a Includes bibliographical references (pages 264-266) and index. | ||
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| 520 | |a Theory of partial differential equations. | ||
| 505 | 0 | |a Front Cover; Theory of Partial Differential Equations; Copyright Page; Contents; PREFACE; PART I: AN OUTLINE; Chapter 1. The Theory of Characteristics, Classification, and the Wave Equation in E2; 1. D' Alembert Solution of the Cauchy Problem for the Homogeneous Wave Equation in E2; 2. Nomenclature; 3. Theory of Characteristics and Type Classification for Equations in E2; 4. Considerations Special to Nonlinear Cases; 5. Compatibility Relations and the Finite-Difference Method of Characteristics; 6. Systems Larger Than Two by Two; 7. Flow and Transmission Line Equations | |
| 505 | 8 | |a Chapter 2. Various Boundary-Value Problems for the Homogeneous Wave Equation in E21. The Cauchy or Initial-Value Problem; 2. The Characteristic Boundary-Value Problem; 3. The Mixed Boundary-Value Problem; 4. The Goursat Problem; 5. The Vibrating String Problem; 6. Uniqueness of the Vibrating String Problem; 7. The Dirichlet Problem for the Wave Equation?; Chapter 3. Various Boundary-Value Problems for the Laplace Equation in E2; 1. The Dirichlet Problem; 2. Relation to Analytic Functions of a Complex Variable; 3. Solution of the Dirichlet Problem on a Circle | |
| 505 | 8 | |a 4. Uniqueness for Regular Solutions of the Dirichlet and Neumann Problem on a Rectangle5. Approximation Methods for the Dirichlet Problem in E2; 6. The Cauchy Problem for the Laplace Equation; Chapter 4. Various Boundary-Value Problems for Simple Equations of Parabolic Type; 1. The Slab Problem; 2. An Alternative Proof of Uniqueness; 3. Solution by Separation of Variables; 4. Instability for Negative Times; 5. Cauchy Problem on the Infinite Line; 6. Unique Continuation; 7. Poiseuille Flow; 8. Mean-Square Asymptotic Uniqueness | |
| 505 | 8 | |a 9. Solution of a Dirichlet Problem for an Equation of Parabolic TypeChapter 5. Expectations for Well-Posed Problems; 1. Sense of Hadamard; 2. Expectations; 3. Boundary-Value Problems for Equations of Elliptic-Parabolic Type; 4. Existence as the Limit of Regular Solutions; 5. The Impulse Problem as a Prototype of a Solution in Terms of Distributions; 6. The Green Identities; 7. The Generalized Green Identity; 8. Lp-Weak Solutions; 9. Prospectus; 10. The Tricomi Problem; PART II: SOME CLASSICAL RESULTS FOR NONLINEAR EQUATIONS IN TWO INDEPENDENT VARIABLES | |
| 505 | 8 | |a Chapter 6. Existence and Uniqueness Considerations for the Nonhomogeneous Wave Equation in E21. Notation; 2. Existence for the Characteristic Problem; 3. Comments on Continuous Dependence and Error Bounds; 4. An Example Where the Theorem as Stated Does Not Apply; 5. A Theorem Using the Lipschitz Condition on a Bounded Region in E5; 6. Existence Theorem for the Cauchy Problem of the Nonhomogeneous (Nonlinear) Wave Equation in E2; Chapter 7. The Riemann Method; 1. Three Forms of the Generalized Green Identity; 2. Riemann's Function | |
| 650 | 0 | |a Differential equations, Partial. |0 http://id.loc.gov/authorities/subjects/sh85037912 | |
| 650 | 6 | |a Équations aux dérivées partielles. | |
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| 650 | 7 | |a Differential equations, Partial |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Lieberstein, H. Melvin. |t Theory of partial differential equations. |d New York, Academic Press, 1972 |z 9780124495500 |w (DLC) 72084278 |w (OCoLC)482715 |
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| author | Lieberstein, H. Melvin |
| author_GND | http://id.loc.gov/authorities/names/n88669037 |
| author_facet | Lieberstein, H. Melvin |
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| author_sort | Lieberstein, H. Melvin |
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| building | Verbundindex |
| bvnumber | localFWS |
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| callnumber-label | QA374 |
| callnumber-raw | QA374 .L45 1972eb |
| callnumber-search | QA374 .L45 1972eb |
| callnumber-sort | QA 3374 L45 41972EB |
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| contents | Front Cover; Theory of Partial Differential Equations; Copyright Page; Contents; PREFACE; PART I: AN OUTLINE; Chapter 1. The Theory of Characteristics, Classification, and the Wave Equation in E2; 1. D' Alembert Solution of the Cauchy Problem for the Homogeneous Wave Equation in E2; 2. Nomenclature; 3. Theory of Characteristics and Type Classification for Equations in E2; 4. Considerations Special to Nonlinear Cases; 5. Compatibility Relations and the Finite-Difference Method of Characteristics; 6. Systems Larger Than Two by Two; 7. Flow and Transmission Line Equations Chapter 2. Various Boundary-Value Problems for the Homogeneous Wave Equation in E21. The Cauchy or Initial-Value Problem; 2. The Characteristic Boundary-Value Problem; 3. The Mixed Boundary-Value Problem; 4. The Goursat Problem; 5. The Vibrating String Problem; 6. Uniqueness of the Vibrating String Problem; 7. The Dirichlet Problem for the Wave Equation?; Chapter 3. Various Boundary-Value Problems for the Laplace Equation in E2; 1. The Dirichlet Problem; 2. Relation to Analytic Functions of a Complex Variable; 3. Solution of the Dirichlet Problem on a Circle 4. Uniqueness for Regular Solutions of the Dirichlet and Neumann Problem on a Rectangle5. Approximation Methods for the Dirichlet Problem in E2; 6. The Cauchy Problem for the Laplace Equation; Chapter 4. Various Boundary-Value Problems for Simple Equations of Parabolic Type; 1. The Slab Problem; 2. An Alternative Proof of Uniqueness; 3. Solution by Separation of Variables; 4. Instability for Negative Times; 5. Cauchy Problem on the Infinite Line; 6. Unique Continuation; 7. Poiseuille Flow; 8. Mean-Square Asymptotic Uniqueness 9. Solution of a Dirichlet Problem for an Equation of Parabolic TypeChapter 5. Expectations for Well-Posed Problems; 1. Sense of Hadamard; 2. Expectations; 3. Boundary-Value Problems for Equations of Elliptic-Parabolic Type; 4. Existence as the Limit of Regular Solutions; 5. The Impulse Problem as a Prototype of a Solution in Terms of Distributions; 6. The Green Identities; 7. The Generalized Green Identity; 8. Lp-Weak Solutions; 9. Prospectus; 10. The Tricomi Problem; PART II: SOME CLASSICAL RESULTS FOR NONLINEAR EQUATIONS IN TWO INDEPENDENT VARIABLES Chapter 6. Existence and Uniqueness Considerations for the Nonhomogeneous Wave Equation in E21. Notation; 2. Existence for the Characteristic Problem; 3. Comments on Continuous Dependence and Error Bounds; 4. An Example Where the Theorem as Stated Does Not Apply; 5. A Theorem Using the Lipschitz Condition on a Bounded Region in E5; 6. Existence Theorem for the Cauchy Problem of the Nonhomogeneous (Nonlinear) Wave Equation in E2; Chapter 7. The Riemann Method; 1. Three Forms of the Generalized Green Identity; 2. Riemann's Function |
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| id | ZDB-4-EBA-ocn316552945 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:42Z |
| institution | BVB |
| isbn | 9780124495500 0124495508 9780080956022 0080956025 1282290398 9781282290396 |
| language | English |
| oclc_num | 316552945 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiv, 283 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Academic Press, |
| record_format | marc |
| series | Mathematics in science and engineering ; |
| series2 | Mathematics in science and engineering ; |
| spelling | Lieberstein, H. Melvin. http://id.loc.gov/authorities/names/n88669037 Theory of partial differential equations / H. Melvin Lieberstein. New York : Academic Press, 1972. 1 online resource (xiv, 283 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics in science and engineering ; v. 93 Includes bibliographical references (pages 264-266) and index. Print version record. Theory of partial differential equations. Front Cover; Theory of Partial Differential Equations; Copyright Page; Contents; PREFACE; PART I: AN OUTLINE; Chapter 1. The Theory of Characteristics, Classification, and the Wave Equation in E2; 1. D' Alembert Solution of the Cauchy Problem for the Homogeneous Wave Equation in E2; 2. Nomenclature; 3. Theory of Characteristics and Type Classification for Equations in E2; 4. Considerations Special to Nonlinear Cases; 5. Compatibility Relations and the Finite-Difference Method of Characteristics; 6. Systems Larger Than Two by Two; 7. Flow and Transmission Line Equations Chapter 2. Various Boundary-Value Problems for the Homogeneous Wave Equation in E21. The Cauchy or Initial-Value Problem; 2. The Characteristic Boundary-Value Problem; 3. The Mixed Boundary-Value Problem; 4. The Goursat Problem; 5. The Vibrating String Problem; 6. Uniqueness of the Vibrating String Problem; 7. The Dirichlet Problem for the Wave Equation?; Chapter 3. Various Boundary-Value Problems for the Laplace Equation in E2; 1. The Dirichlet Problem; 2. Relation to Analytic Functions of a Complex Variable; 3. Solution of the Dirichlet Problem on a Circle 4. Uniqueness for Regular Solutions of the Dirichlet and Neumann Problem on a Rectangle5. Approximation Methods for the Dirichlet Problem in E2; 6. The Cauchy Problem for the Laplace Equation; Chapter 4. Various Boundary-Value Problems for Simple Equations of Parabolic Type; 1. The Slab Problem; 2. An Alternative Proof of Uniqueness; 3. Solution by Separation of Variables; 4. Instability for Negative Times; 5. Cauchy Problem on the Infinite Line; 6. Unique Continuation; 7. Poiseuille Flow; 8. Mean-Square Asymptotic Uniqueness 9. Solution of a Dirichlet Problem for an Equation of Parabolic TypeChapter 5. Expectations for Well-Posed Problems; 1. Sense of Hadamard; 2. Expectations; 3. Boundary-Value Problems for Equations of Elliptic-Parabolic Type; 4. Existence as the Limit of Regular Solutions; 5. The Impulse Problem as a Prototype of a Solution in Terms of Distributions; 6. The Green Identities; 7. The Generalized Green Identity; 8. Lp-Weak Solutions; 9. Prospectus; 10. The Tricomi Problem; PART II: SOME CLASSICAL RESULTS FOR NONLINEAR EQUATIONS IN TWO INDEPENDENT VARIABLES Chapter 6. Existence and Uniqueness Considerations for the Nonhomogeneous Wave Equation in E21. Notation; 2. Existence for the Characteristic Problem; 3. Comments on Continuous Dependence and Error Bounds; 4. An Example Where the Theorem as Stated Does Not Apply; 5. A Theorem Using the Lipschitz Condition on a Bounded Region in E5; 6. Existence Theorem for the Cauchy Problem of the Nonhomogeneous (Nonlinear) Wave Equation in E2; Chapter 7. The Riemann Method; 1. Three Forms of the Generalized Green Identity; 2. Riemann's Function Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Équations aux dérivées partielles. MATHEMATICS Differential Equations Partial. bisacsh Differential equations, Partial fast Print version: Lieberstein, H. Melvin. Theory of partial differential equations. New York, Academic Press, 1972 9780124495500 (DLC) 72084278 (OCoLC)482715 Mathematics in science and engineering ; v. 93. 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=297117 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://www.sciencedirect.com/science/bookseries/00765392/93 Volltext |
| spellingShingle | Lieberstein, H. Melvin Theory of partial differential equations / Mathematics in science and engineering ; Front Cover; Theory of Partial Differential Equations; Copyright Page; Contents; PREFACE; PART I: AN OUTLINE; Chapter 1. The Theory of Characteristics, Classification, and the Wave Equation in E2; 1. D' Alembert Solution of the Cauchy Problem for the Homogeneous Wave Equation in E2; 2. Nomenclature; 3. Theory of Characteristics and Type Classification for Equations in E2; 4. Considerations Special to Nonlinear Cases; 5. Compatibility Relations and the Finite-Difference Method of Characteristics; 6. Systems Larger Than Two by Two; 7. Flow and Transmission Line Equations Chapter 2. Various Boundary-Value Problems for the Homogeneous Wave Equation in E21. The Cauchy or Initial-Value Problem; 2. The Characteristic Boundary-Value Problem; 3. The Mixed Boundary-Value Problem; 4. The Goursat Problem; 5. The Vibrating String Problem; 6. Uniqueness of the Vibrating String Problem; 7. The Dirichlet Problem for the Wave Equation?; Chapter 3. Various Boundary-Value Problems for the Laplace Equation in E2; 1. The Dirichlet Problem; 2. Relation to Analytic Functions of a Complex Variable; 3. Solution of the Dirichlet Problem on a Circle 4. Uniqueness for Regular Solutions of the Dirichlet and Neumann Problem on a Rectangle5. Approximation Methods for the Dirichlet Problem in E2; 6. The Cauchy Problem for the Laplace Equation; Chapter 4. Various Boundary-Value Problems for Simple Equations of Parabolic Type; 1. The Slab Problem; 2. An Alternative Proof of Uniqueness; 3. Solution by Separation of Variables; 4. Instability for Negative Times; 5. Cauchy Problem on the Infinite Line; 6. Unique Continuation; 7. Poiseuille Flow; 8. Mean-Square Asymptotic Uniqueness 9. Solution of a Dirichlet Problem for an Equation of Parabolic TypeChapter 5. Expectations for Well-Posed Problems; 1. Sense of Hadamard; 2. Expectations; 3. Boundary-Value Problems for Equations of Elliptic-Parabolic Type; 4. Existence as the Limit of Regular Solutions; 5. The Impulse Problem as a Prototype of a Solution in Terms of Distributions; 6. The Green Identities; 7. The Generalized Green Identity; 8. Lp-Weak Solutions; 9. Prospectus; 10. The Tricomi Problem; PART II: SOME CLASSICAL RESULTS FOR NONLINEAR EQUATIONS IN TWO INDEPENDENT VARIABLES Chapter 6. Existence and Uniqueness Considerations for the Nonhomogeneous Wave Equation in E21. Notation; 2. Existence for the Characteristic Problem; 3. Comments on Continuous Dependence and Error Bounds; 4. An Example Where the Theorem as Stated Does Not Apply; 5. A Theorem Using the Lipschitz Condition on a Bounded Region in E5; 6. Existence Theorem for the Cauchy Problem of the Nonhomogeneous (Nonlinear) Wave Equation in E2; Chapter 7. The Riemann Method; 1. Three Forms of the Generalized Green Identity; 2. Riemann's Function Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Équations aux dérivées partielles. MATHEMATICS Differential Equations Partial. bisacsh Differential equations, Partial fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85037912 |
| title | Theory of partial differential equations / |
| title_auth | Theory of partial differential equations / |
| title_exact_search | Theory of partial differential equations / |
| title_full | Theory of partial differential equations / H. Melvin Lieberstein. |
| title_fullStr | Theory of partial differential equations / H. Melvin Lieberstein. |
| title_full_unstemmed | Theory of partial differential equations / H. Melvin Lieberstein. |
| title_short | Theory of partial differential equations / |
| title_sort | theory of partial differential equations |
| topic | Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Équations aux dérivées partielles. MATHEMATICS Differential Equations Partial. bisacsh Differential equations, Partial fast |
| topic_facet | Differential equations, Partial. Équations aux dérivées partielles. MATHEMATICS Differential Equations Partial. Differential equations, Partial |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297117 https://www.sciencedirect.com/science/bookseries/00765392/93 |
| work_keys_str_mv | AT liebersteinhmelvin theoryofpartialdifferentialequations |