Advanced engineering analysis: the calculus of variations and functional analysis with applications in mechanics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
2012
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and index 1. Basic calculus of variations. 1.1. Introduction. 1.2. Euler's equation for the simplest problem. 1.3. Properties of extremals of the simplest functional. 1.4. Ritz's method. 1.5. Natural boundary conditions. 1.6. Extensions to more general functionals. 1.7. Functionals depending on functions in many variables. 1.8. A functional with integrand depending on partial derivatives of higher order. 1.9. The first variation. 1.10. Isoperimetric problems. 1.11. General form of the first variation. 1.12. Movable ends of extremals. 1.13. Broken extremals: Weierstrass-Erdmann conditions and related problems. 1.14. Sufficient conditions for minimum. 1.15. Exercises -- 2. Applications of the calculus of variations in mechanics. 2.1. Elementary problems for elastic structures. 2.2. Some extremal principles of mechanics. 2.3. Conservation laws. 2.4. Conservation laws and Noether's theorem. 2.5. Functionals depending on higher derivatives of y. 2.6. Noether's theorem, general case. 2.7. Generalizations. 2.8. Exercises -- 3. Elements of optimal control theory. 3.1. A variational problem as an optimal control problem. 3.2. General problem of optimal control. 3.3. Simplest problem of optimal control. 3.4. Fundamental solution of a linear ordinary differential equation. 3.5. The simplest problem, continued. 3.6. Pontryagin's maximum principle for the simplest problem. 3.7. Some mathematical preliminaries. 3.8. General terminal control problem. 3.9. Pontryagin's maximum principle for the terminal optimal problem. 3.10. Generalization of the terminal control problem. 3.11. Small variations of control function for terminal control problem. 3.12. A discrete version of small variations of control function for generalized terminal control problem. 3.13. Optimal time control problems. 3.14. Final remarks on control problems. 3.15. Exercises 4. Functional analysis. 4.1. A normed space as a metric space. 4.2. Dimension of a linear space and separability. 4.3. Cauchy sequences and Banach spaces. 4.4. The completion theorem. 4.5. L[symbol] spaces and the Lebesgue integral. 4.6. Sobolev spaces. 4.7. Compactness. 4.8. Inner product spaces, Hilbert spaces. 4.9. Operators and functionals. 4.10. Contraction mapping principle. 4.11. Some approximation theory. 4.12 Orthogonal decomposition of a Hilbert space and the Riesz representation theorem. 4.13. Basis, Gram-Schmidt procedure, and Fourier series in Hilbert space. 4.14. Weak convergence. 4.15. Adjoint and self-adjoint operators. 4.16. Compact operators. 4.17. Closed operators. 4.18. On the Sobolev imbedding theorem. 4.19. Some energy spaces in mechanics. 4.20. Introduction to spectral concepts. 4.21. The Fredholm theory in Hilbert spaces. 4.22. Exercises -- 5. Applications of functional analysis in mechanics. 5.1. Some mechanics problems from the standpoint of the calculus of variations; the virtual work principle. 5.2. Generalized solution of the equilibrium problem for a clamped rod with springs. 5.3. Equilibrium problem for a clamped membrane and its generalized solution. 5.4. Equilibrium of a free membrane. 5.5. Some other equilibrium problems of linear mechanics. 5.6. The Ritz and Bubnov-Galerkin methods. 5.7. The Hamilton-Ostrogradski principle and generalized setup of dynamical problems in classical mechanics. 5.8. Generalized setup of dynamic problem for membrane. 5.9. Other dynamic problems of linear mechanics. 5.10. The Fourier method. 5.11. An eigenfrequency boundary value problem arising in linear mechanics. 5.12. The spectral theorem. 5.13. The Fourier method, continued. 5.14. Equilibrium of a von Karman plate. 5.15. A unilateral problem. 5.16. Exercises Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study |
| Beschreibung: | 1 Online-Ressource (x, 489 p. :) |
| ISBN: | 9789814390484 9814390488 |
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| 245 | 1 | 0 | |a Advanced engineering analysis |b the calculus of variations and functional analysis with applications in mechanics |c Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev |
| 264 | 1 | |a Singapore |b World Scientific Pub. Co. |c 2012 | |
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| 500 | |a Includes bibliographical references and index | ||
| 500 | |a 1. Basic calculus of variations. 1.1. Introduction. 1.2. Euler's equation for the simplest problem. 1.3. Properties of extremals of the simplest functional. 1.4. Ritz's method. 1.5. Natural boundary conditions. 1.6. Extensions to more general functionals. 1.7. Functionals depending on functions in many variables. 1.8. A functional with integrand depending on partial derivatives of higher order. 1.9. The first variation. 1.10. Isoperimetric problems. 1.11. General form of the first variation. 1.12. Movable ends of extremals. 1.13. Broken extremals: Weierstrass-Erdmann conditions and related problems. 1.14. Sufficient conditions for minimum. 1.15. Exercises -- 2. Applications of the calculus of variations in mechanics. 2.1. Elementary problems for elastic structures. 2.2. Some extremal principles of mechanics. 2.3. Conservation laws. 2.4. Conservation laws and Noether's theorem. 2.5. Functionals depending on higher derivatives of y. 2.6. Noether's theorem, general case. 2.7. Generalizations. 2.8. Exercises -- 3. Elements of optimal control theory. 3.1. A variational problem as an optimal control problem. 3.2. General problem of optimal control. 3.3. Simplest problem of optimal control. 3.4. Fundamental solution of a linear ordinary differential equation. 3.5. The simplest problem, continued. 3.6. Pontryagin's maximum principle for the simplest problem. 3.7. Some mathematical preliminaries. 3.8. General terminal control problem. 3.9. Pontryagin's maximum principle for the terminal optimal problem. 3.10. Generalization of the terminal control problem. 3.11. Small variations of control function for terminal control problem. 3.12. A discrete version of small variations of control function for generalized terminal control problem. 3.13. Optimal time control problems. 3.14. Final remarks on control problems. 3.15. Exercises | ||
| 500 | |a 4. Functional analysis. 4.1. A normed space as a metric space. 4.2. Dimension of a linear space and separability. 4.3. Cauchy sequences and Banach spaces. 4.4. The completion theorem. 4.5. L[symbol] spaces and the Lebesgue integral. 4.6. Sobolev spaces. 4.7. Compactness. 4.8. Inner product spaces, Hilbert spaces. 4.9. Operators and functionals. 4.10. Contraction mapping principle. 4.11. Some approximation theory. 4.12 Orthogonal decomposition of a Hilbert space and the Riesz representation theorem. 4.13. Basis, Gram-Schmidt procedure, and Fourier series in Hilbert space. 4.14. Weak convergence. 4.15. Adjoint and self-adjoint operators. 4.16. Compact operators. 4.17. Closed operators. 4.18. On the Sobolev imbedding theorem. 4.19. Some energy spaces in mechanics. 4.20. Introduction to spectral concepts. 4.21. The Fredholm theory in Hilbert spaces. 4.22. Exercises -- 5. Applications of functional analysis in mechanics. 5.1. Some mechanics problems from the standpoint of the calculus of variations; the virtual work principle. 5.2. Generalized solution of the equilibrium problem for a clamped rod with springs. 5.3. Equilibrium problem for a clamped membrane and its generalized solution. 5.4. Equilibrium of a free membrane. 5.5. Some other equilibrium problems of linear mechanics. 5.6. The Ritz and Bubnov-Galerkin methods. 5.7. The Hamilton-Ostrogradski principle and generalized setup of dynamical problems in classical mechanics. 5.8. Generalized setup of dynamic problem for membrane. 5.9. Other dynamic problems of linear mechanics. 5.10. The Fourier method. 5.11. An eigenfrequency boundary value problem arising in linear mechanics. 5.12. The spectral theorem. 5.13. The Fourier method, continued. 5.14. Equilibrium of a von Karman plate. 5.15. A unilateral problem. 5.16. Exercises | ||
| 500 | |a Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study | ||
| 650 | 7 | |a TECHNOLOGY & ENGINEERING / Mechanical |2 bisacsh | |
| 650 | 4 | |a Engineering mathematics | |
| 650 | 4 | |a Calculus | |
| 650 | 4 | |a Mechanics | |
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| 700 | 1 | |a Cloud, Michael J. |e Sonstige |4 oth | |
| 700 | 1 | |a Eremeyev, Victor A. |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804175624503296000 |
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| any_adam_object | |
| author | Lebedev, L. P. |
| author_facet | Lebedev, L. P. |
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| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 621 - Applied physics |
| dewey-raw | 621 |
| dewey-search | 621 |
| dewey-sort | 3621 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Technik Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043157645 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:19:15Z |
| institution | BVB |
| isbn | 9789814390484 9814390488 |
| language | English |
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| spelling | Lebedev, L. P. Verfasser aut Advanced engineering analysis the calculus of variations and functional analysis with applications in mechanics Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev Singapore World Scientific Pub. Co. 2012 1 Online-Ressource (x, 489 p. :) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references and index 1. Basic calculus of variations. 1.1. Introduction. 1.2. Euler's equation for the simplest problem. 1.3. Properties of extremals of the simplest functional. 1.4. Ritz's method. 1.5. Natural boundary conditions. 1.6. Extensions to more general functionals. 1.7. Functionals depending on functions in many variables. 1.8. A functional with integrand depending on partial derivatives of higher order. 1.9. The first variation. 1.10. Isoperimetric problems. 1.11. General form of the first variation. 1.12. Movable ends of extremals. 1.13. Broken extremals: Weierstrass-Erdmann conditions and related problems. 1.14. Sufficient conditions for minimum. 1.15. Exercises -- 2. Applications of the calculus of variations in mechanics. 2.1. Elementary problems for elastic structures. 2.2. Some extremal principles of mechanics. 2.3. Conservation laws. 2.4. Conservation laws and Noether's theorem. 2.5. Functionals depending on higher derivatives of y. 2.6. Noether's theorem, general case. 2.7. Generalizations. 2.8. Exercises -- 3. Elements of optimal control theory. 3.1. A variational problem as an optimal control problem. 3.2. General problem of optimal control. 3.3. Simplest problem of optimal control. 3.4. Fundamental solution of a linear ordinary differential equation. 3.5. The simplest problem, continued. 3.6. Pontryagin's maximum principle for the simplest problem. 3.7. Some mathematical preliminaries. 3.8. General terminal control problem. 3.9. Pontryagin's maximum principle for the terminal optimal problem. 3.10. Generalization of the terminal control problem. 3.11. Small variations of control function for terminal control problem. 3.12. A discrete version of small variations of control function for generalized terminal control problem. 3.13. Optimal time control problems. 3.14. Final remarks on control problems. 3.15. Exercises 4. Functional analysis. 4.1. A normed space as a metric space. 4.2. Dimension of a linear space and separability. 4.3. Cauchy sequences and Banach spaces. 4.4. The completion theorem. 4.5. L[symbol] spaces and the Lebesgue integral. 4.6. Sobolev spaces. 4.7. Compactness. 4.8. Inner product spaces, Hilbert spaces. 4.9. Operators and functionals. 4.10. Contraction mapping principle. 4.11. Some approximation theory. 4.12 Orthogonal decomposition of a Hilbert space and the Riesz representation theorem. 4.13. Basis, Gram-Schmidt procedure, and Fourier series in Hilbert space. 4.14. Weak convergence. 4.15. Adjoint and self-adjoint operators. 4.16. Compact operators. 4.17. Closed operators. 4.18. On the Sobolev imbedding theorem. 4.19. Some energy spaces in mechanics. 4.20. Introduction to spectral concepts. 4.21. The Fredholm theory in Hilbert spaces. 4.22. Exercises -- 5. Applications of functional analysis in mechanics. 5.1. Some mechanics problems from the standpoint of the calculus of variations; the virtual work principle. 5.2. Generalized solution of the equilibrium problem for a clamped rod with springs. 5.3. Equilibrium problem for a clamped membrane and its generalized solution. 5.4. Equilibrium of a free membrane. 5.5. Some other equilibrium problems of linear mechanics. 5.6. The Ritz and Bubnov-Galerkin methods. 5.7. The Hamilton-Ostrogradski principle and generalized setup of dynamical problems in classical mechanics. 5.8. Generalized setup of dynamic problem for membrane. 5.9. Other dynamic problems of linear mechanics. 5.10. The Fourier method. 5.11. An eigenfrequency boundary value problem arising in linear mechanics. 5.12. The spectral theorem. 5.13. The Fourier method, continued. 5.14. Equilibrium of a von Karman plate. 5.15. A unilateral problem. 5.16. Exercises Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study TECHNOLOGY & ENGINEERING / Mechanical bisacsh Engineering mathematics Calculus Mechanics Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Strukturmechanik (DE-588)4126904-4 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s Strukturmechanik (DE-588)4126904-4 s Strömungsmechanik (DE-588)4077970-1 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Cloud, Michael J. Sonstige oth Eremeyev, Victor A. Sonstige oth Erscheint auch als Druckausgabe 978-981-4390-47-7 Erscheint auch als Druckausgabe 981-4390-47-X http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457240 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lebedev, L. P. Advanced engineering analysis the calculus of variations and functional analysis with applications in mechanics TECHNOLOGY & ENGINEERING / Mechanical bisacsh Engineering mathematics Calculus Mechanics Funktionalanalysis (DE-588)4018916-8 gnd Strukturmechanik (DE-588)4126904-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4126904-4 (DE-588)4128130-5 (DE-588)4077970-1 |
| title | Advanced engineering analysis the calculus of variations and functional analysis with applications in mechanics |
| title_auth | Advanced engineering analysis the calculus of variations and functional analysis with applications in mechanics |
| title_exact_search | Advanced engineering analysis the calculus of variations and functional analysis with applications in mechanics |
| title_full | Advanced engineering analysis the calculus of variations and functional analysis with applications in mechanics Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev |
| title_fullStr | Advanced engineering analysis the calculus of variations and functional analysis with applications in mechanics Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev |
| title_full_unstemmed | Advanced engineering analysis the calculus of variations and functional analysis with applications in mechanics Leonid P. Lebedev, Michael J. Cloud, Victor A. Eremeyev |
| title_short | Advanced engineering analysis |
| title_sort | advanced engineering analysis the calculus of variations and functional analysis with applications in mechanics |
| title_sub | the calculus of variations and functional analysis with applications in mechanics |
| topic | TECHNOLOGY & ENGINEERING / Mechanical bisacsh Engineering mathematics Calculus Mechanics Funktionalanalysis (DE-588)4018916-8 gnd Strukturmechanik (DE-588)4126904-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | TECHNOLOGY & ENGINEERING / Mechanical Engineering mathematics Calculus Mechanics Funktionalanalysis Strukturmechanik Numerisches Verfahren Strömungsmechanik |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457240 |
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