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Differential geometric methods in the control of partial differential equations : 1999 AMS-IMS-SIAM Joint Summer Research Conference on Differential Geometric Methods in the Control of Partial Differential Equations, University of Colorado, Boulder, June 27-July 1, 1999 / / Robert Gulliver, Walter Littman, Roberto Triggiani, editors
| Differential geometric methods in the control of partial differential equations : 1999 AMS-IMS-SIAM Joint Summer Research Conference on Differential Geometric Methods in the Control of Partial Differential Equations, University of Colorado, Boulder, June 27-July 1, 1999 / / Robert Gulliver, Walter Littman, Roberto Triggiani, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (418 p.) |
| Disciplina | 515/.35 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Boundary value problems - Numerical solutions
Differential equations, Partial - Numerical solutions Geometry, Differential |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-8218-7858-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Wellposedness of a structural acoustics model with point control""; ""Intrinsic geometric model for the vibration of a constrained shell""; ""A noise reduction problem arising in structural acoustics: A three-dimensional solution""; ""The free boundary problem in the optimization of composite membranes""; ""Tangential differential calculus and functional analysis on a C1,1 submanifold""; ""Carleman estimates with two large parameters and applications""; ""On the prescribed Scalar curvature problem on compact manifolds with boundary""
""Chord uniqueness and controllability: The view from the boundary, I""""Nonlinear boundary stabilization of a system of anisotropic elasticity with light internal damping""; ""Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse hyperbolic problems""; ""Nonconservative wave equations with unobserved Neumann B. C.: Global uniqueness and observability in one shot""; ""Uniform stability of a coupled structural acoustic system with thermoelastic effects and weak structural damping"" ""Topological derivative for nucleation of non-circular voids. The Neumann problem""""Remarks on global uniqueness theorems for partial differential equations""; ""Evolution of a graph by Levi form""; ""Observability inequalities for the Euler-Bernoulli plate with variable coefficients"" |
| Record Nr. | UNINA-9910480262403321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential geometric methods in the control of partial differential equations : 1999 AMS-IMS-SIAM Joint Summer Research Conference on Differential Geometric Methods in the Control of Partial Differential Equations, University of Colorado, Boulder, June 27-July 1, 1999 / / Robert Gulliver, Walter Littman, Roberto Triggiani, editors
| Differential geometric methods in the control of partial differential equations : 1999 AMS-IMS-SIAM Joint Summer Research Conference on Differential Geometric Methods in the Control of Partial Differential Equations, University of Colorado, Boulder, June 27-July 1, 1999 / / Robert Gulliver, Walter Littman, Roberto Triggiani, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (418 p.) |
| Disciplina | 515/.35 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Boundary value problems - Numerical solutions
Differential equations, Partial - Numerical solutions Geometry, Differential |
| ISBN | 0-8218-7858-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Wellposedness of a structural acoustics model with point control""; ""Intrinsic geometric model for the vibration of a constrained shell""; ""A noise reduction problem arising in structural acoustics: A three-dimensional solution""; ""The free boundary problem in the optimization of composite membranes""; ""Tangential differential calculus and functional analysis on a C1,1 submanifold""; ""Carleman estimates with two large parameters and applications""; ""On the prescribed Scalar curvature problem on compact manifolds with boundary""
""Chord uniqueness and controllability: The view from the boundary, I""""Nonlinear boundary stabilization of a system of anisotropic elasticity with light internal damping""; ""Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse hyperbolic problems""; ""Nonconservative wave equations with unobserved Neumann B. C.: Global uniqueness and observability in one shot""; ""Uniform stability of a coupled structural acoustic system with thermoelastic effects and weak structural damping"" ""Topological derivative for nucleation of non-circular voids. The Neumann problem""""Remarks on global uniqueness theorems for partial differential equations""; ""Evolution of a graph by Levi form""; ""Observability inequalities for the Euler-Bernoulli plate with variable coefficients"" |
| Record Nr. | UNINA-9910788655103321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential geometric methods in the control of partial differential equations : 1999 AMS-IMS-SIAM Joint Summer Research Conference on Differential Geometric Methods in the Control of Partial Differential Equations, University of Colorado, Boulder, June 27-July 1, 1999 / / Robert Gulliver, Walter Littman, Roberto Triggiani, editors
| Differential geometric methods in the control of partial differential equations : 1999 AMS-IMS-SIAM Joint Summer Research Conference on Differential Geometric Methods in the Control of Partial Differential Equations, University of Colorado, Boulder, June 27-July 1, 1999 / / Robert Gulliver, Walter Littman, Roberto Triggiani, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (418 p.) |
| Disciplina | 515/.35 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Boundary value problems - Numerical solutions
Differential equations, Partial - Numerical solutions Geometry, Differential |
| ISBN | 0-8218-7858-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Wellposedness of a structural acoustics model with point control""; ""Intrinsic geometric model for the vibration of a constrained shell""; ""A noise reduction problem arising in structural acoustics: A three-dimensional solution""; ""The free boundary problem in the optimization of composite membranes""; ""Tangential differential calculus and functional analysis on a C1,1 submanifold""; ""Carleman estimates with two large parameters and applications""; ""On the prescribed Scalar curvature problem on compact manifolds with boundary""
""Chord uniqueness and controllability: The view from the boundary, I""""Nonlinear boundary stabilization of a system of anisotropic elasticity with light internal damping""; ""Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse hyperbolic problems""; ""Nonconservative wave equations with unobserved Neumann B. C.: Global uniqueness and observability in one shot""; ""Uniform stability of a coupled structural acoustic system with thermoelastic effects and weak structural damping"" ""Topological derivative for nucleation of non-circular voids. The Neumann problem""""Remarks on global uniqueness theorems for partial differential equations""; ""Evolution of a graph by Levi form""; ""Observability inequalities for the Euler-Bernoulli plate with variable coefficients"" |
| Record Nr. | UNINA-9910817969503321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The finite element method for boundary value problems : mathematics and computations / / Karan S. Surana and J.N. Reddy
| The finite element method for boundary value problems : mathematics and computations / / Karan S. Surana and J.N. Reddy |
| Autore | Surana Karan S. |
| Pubbl/distr/stampa | Boca Raton : , : CRC Press, , [2017] |
| Descrizione fisica | 1 online resource (820 pages) : illustrations |
| Disciplina | 515/.62 |
| Soggetto topico |
Boundary value problems - Numerical solutions
Finite element method |
| ISBN |
1-315-36571-5
1-4987-8050-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Introduction -- 2. Concepts from functional analysis -- 3. Classical methods of approximation -- 4. The finite element method -- 5. Self-adjoint differential operators -- 6. Non-self-adjoint differential operators -- 7. Non-linear differential operators -- 8. Basic elements of mapping and interpolation theory -- 9. Linear elasticity using the principle of minimum total potential energy -- 10. Linear and nonlinear solid mechanics using the principle of virtual displacements -- 11. Additional topics in linear structural mechanics -- 12. Convergence, error estimation, and adaptivity. |
| Record Nr. | UNINA-9910151566303321 |
Surana Karan S.
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| Boca Raton : , : CRC Press, , [2017] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite elements in vector lattices / / Martin R. Weber
| Finite elements in vector lattices / / Martin R. Weber |
| Autore | Weber Martin R. |
| Pubbl/distr/stampa | Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2014 |
| Descrizione fisica | 1 online resource (230 p.) |
| Disciplina | 515.35 |
| Soggetto topico | Boundary value problems - Numerical solutions |
| Soggetto genere / forma | Electronic books. |
| ISBN |
3-11-037827-2
3-11-035078-5 |
| Classificazione | SK 600 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- 1. Introduction -- 2. Ordered vector spaces and vector lattices -- 3. Finite, totally finite and self majorizing elements in Archimedean vector lattices -- 4. Finite elements in vector lattices of linear operators -- 5. The space of maximal ideals of a vector lattice -- 6. Topological characterization of finite elements -- 7. Representations of vector lattices and their properties -- 8. Vector lattices of continuous functions with finite elements -- 9. Representations of vector lattices by means of continuous functions -- 10. Representations of vector lattices by means of bases of finite elements -- List of Examples -- List of Symbols -- Bibliography -- Index |
| Record Nr. | UNINA-9910463847603321 |
|
Weber Martin R.
|
||
| Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite elements in vector lattices / / Martin R. Weber
| Finite elements in vector lattices / / Martin R. Weber |
| Autore | Weber Martin R. |
| Pubbl/distr/stampa | Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2014 |
| Descrizione fisica | 1 online resource (230 p.) |
| Disciplina | 515.35 |
| Soggetto topico | Boundary value problems - Numerical solutions |
| ISBN |
3-11-037827-2
3-11-035078-5 |
| Classificazione | SK 600 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- 1. Introduction -- 2. Ordered vector spaces and vector lattices -- 3. Finite, totally finite and self majorizing elements in Archimedean vector lattices -- 4. Finite elements in vector lattices of linear operators -- 5. The space of maximal ideals of a vector lattice -- 6. Topological characterization of finite elements -- 7. Representations of vector lattices and their properties -- 8. Vector lattices of continuous functions with finite elements -- 9. Representations of vector lattices by means of continuous functions -- 10. Representations of vector lattices by means of bases of finite elements -- List of Examples -- List of Symbols -- Bibliography -- Index |
| Record Nr. | UNINA-9910788561603321 |
|
Weber Martin R.
|
||
| Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite elements in vector lattices / / Martin R. Weber
| Finite elements in vector lattices / / Martin R. Weber |
| Autore | Weber Martin R. |
| Pubbl/distr/stampa | Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2014 |
| Descrizione fisica | 1 online resource (230 p.) |
| Disciplina | 515.35 |
| Soggetto topico | Boundary value problems - Numerical solutions |
| ISBN |
3-11-037827-2
3-11-035078-5 |
| Classificazione | SK 600 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- 1. Introduction -- 2. Ordered vector spaces and vector lattices -- 3. Finite, totally finite and self majorizing elements in Archimedean vector lattices -- 4. Finite elements in vector lattices of linear operators -- 5. The space of maximal ideals of a vector lattice -- 6. Topological characterization of finite elements -- 7. Representations of vector lattices and their properties -- 8. Vector lattices of continuous functions with finite elements -- 9. Representations of vector lattices by means of continuous functions -- 10. Representations of vector lattices by means of bases of finite elements -- List of Examples -- List of Symbols -- Bibliography -- Index |
| Record Nr. | UNINA-9910813134203321 |
|
Weber Martin R.
|
||
| Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fourier analysis and boundary value problems / / by Enrique A. Gonzalez-Velasco
| Fourier analysis and boundary value problems / / by Enrique A. Gonzalez-Velasco |
| Autore | Gonzalez-Velasco Enrique A |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | San Diego, : Academic Pres, c1995 |
| Descrizione fisica | 1 online resource (565 p.) |
| Disciplina | 515/.353 |
| Soggetto topico |
Fourier analysis
Boundary value problems - Numerical solutions |
| ISBN |
1-281-03822-9
9786611038229 0-08-053193-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Fourier Analysis and Boundary Value Problems; Copyright Page; Table of Contents; Preface; CHAPTER 1. A HEATED DISCUSSION; 1.1 Historical Prologue; 1.2 The Heat Equation; 1.3 Boundary Value Problems; 1.4 The Method of Separation of Variables; 1.5 Linearity and Superposition of Solutions; 1.6 Historical Epilogue; Exercises; CHAPTER 2. FOURIER SERIES; 2.1 Introduction; 2.2 Fourier Series; 2.3 The Riemann-Lebesgue Theorem; 2.4 The Convergence of Fourier Series; 2.5 Fourier Series on Arbitrary Intervals; 2.6 The Gibbs Phenomenon; 2.7 Fejér Sums; 2.8 Integration of Fourier Series
2.9 Historical EpilogueExercises; CHAPTER 3. RETURN TO THE HEATED BAR; 3.1 Existence of a Solution; 3.2 Uniqueness and Stability of the Solution; 3.3 Nonzero Temperature at the Endpoints; 3.4 Bar Insulated at the Endpoints; 3.5 Mixed Endpoint Conditions; 3.6 Heat Convection at One Endpoint; 3.7 Time-Independent Problems; 3.8 The Steady-State Solution; 3.9 The Transient Solution; 3.10 The Complete Solution; 3.11 Time-Dependent Problems; Exercises; CHAPTER 4. GENERALIZED FOURIER SERIES; 4.1 Sturm-Liouville Problems; 4.2 The Eigenvalues and Eigenfunctions; 4.3 The Existence of the Eigenvalues 4.4 Generalized Fourier Series4.5 Approximations; 4.6 Historical Epilogue; Exercises; CHAPTER 5. THE WAVE EQUATION; 5.1 Introduction; 5.2 The Vibrating String; 5.3 D'Alembert's Solution; 5.4 A Struck String; 5.5 Bernoulli's Solution; 5.6 Time-Independent Problems; 5.7 Time-Dependent Problems; 5.8 Historical Epilogue; Exercises; CHAPTER 6. ORTHOGONAL SYSTEMS; 6.1 Fourier Series and Parseval's Identity; 6.2 An Approximation Problem; 6.3 The Uniform Convergence of Fourier Series; 6.4 Convergence in the Mean; 6.5 Applications to the Vibrating String; 6.6 The Riesz-Fischer Theorem; Exercises CHAPTER 7. FOURIER TRANSFORMS7.1 The Laplace Equation; 7.2 Fourier Transforms; 7.3 Properties of the Fourier Transform; 7.4 Convolution; 7.5 Solution of the Dirichlet Problem for the Half-Plane; 7.6 The Fourier Transform Method; Exercises; CHAPTER 8. LAPLACE TRANSFORMS; 8.1 The Laplace Transform and the Inversion Theorem; 8.2 Properties of the Laplace Transform; 8.3 Convolution; 8.4 The Telegraph Equation; 8.5 The Method of Residues; 8.6 Historical Epilogue; Exercises; CHAPTER 9. BOUNDARY VALUE PROBLEMS IN HIGHER DIMENSIONS; 9.1 Electrostatic Potential in a Charged Box 9.2 Double Fourier Series9.3 The Dirichlet Problem in a Box; 9.4 Return to the Charged Box; 9.5 The Multiple Fourier Transform Method; 9.6 The Double Laplace Transform Method; Exercises; CHAPTER 10. BOUNDARY VALUE PROBLEMS WITH CIRCULAR SYMMETRY; 10.1 Vibrations of a Circular Membrane; 10.2 The Gamma Function; 10.3 Bessel Functions of the First Kind; 10.4 Recursion Formulas for Bessel Functions; 10.5 Bessel Functions of the Second Kind; 10.6 The Zeros of Bessel Functions; 10.7 Orthogonal Systems of Bessel Functions; 10.8 Fourier-Bessel Series and Dini-Bessel Series 10.9 Return to the Vibrating Membrane |
| Record Nr. | UNINA-9910826098503321 |
|
Gonzalez-Velasco Enrique A
|
||
| San Diego, : Academic Pres, c1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fourier analysis and boundary value problems [[electronic resource] /] / by Enrique A. González-Velasco
| Fourier analysis and boundary value problems [[electronic resource] /] / by Enrique A. González-Velasco |
| Autore | González-Velasco Enrique A |
| Pubbl/distr/stampa | San Diego, : Academic Pres, c1995 |
| Descrizione fisica | 1 online resource (565 p.) |
| Disciplina | 515/.353 |
| Soggetto topico |
Fourier analysis
Boundary value problems - Numerical solutions |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-03822-9
9786611038229 0-08-053193-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Fourier Analysis and Boundary Value Problems; Copyright Page; Table of Contents; Preface; CHAPTER 1. A HEATED DISCUSSION; 1.1 Historical Prologue; 1.2 The Heat Equation; 1.3 Boundary Value Problems; 1.4 The Method of Separation of Variables; 1.5 Linearity and Superposition of Solutions; 1.6 Historical Epilogue; Exercises; CHAPTER 2. FOURIER SERIES; 2.1 Introduction; 2.2 Fourier Series; 2.3 The Riemann-Lebesgue Theorem; 2.4 The Convergence of Fourier Series; 2.5 Fourier Series on Arbitrary Intervals; 2.6 The Gibbs Phenomenon; 2.7 Fejér Sums; 2.8 Integration of Fourier Series
2.9 Historical EpilogueExercises; CHAPTER 3. RETURN TO THE HEATED BAR; 3.1 Existence of a Solution; 3.2 Uniqueness and Stability of the Solution; 3.3 Nonzero Temperature at the Endpoints; 3.4 Bar Insulated at the Endpoints; 3.5 Mixed Endpoint Conditions; 3.6 Heat Convection at One Endpoint; 3.7 Time-Independent Problems; 3.8 The Steady-State Solution; 3.9 The Transient Solution; 3.10 The Complete Solution; 3.11 Time-Dependent Problems; Exercises; CHAPTER 4. GENERALIZED FOURIER SERIES; 4.1 Sturm-Liouville Problems; 4.2 The Eigenvalues and Eigenfunctions; 4.3 The Existence of the Eigenvalues 4.4 Generalized Fourier Series4.5 Approximations; 4.6 Historical Epilogue; Exercises; CHAPTER 5. THE WAVE EQUATION; 5.1 Introduction; 5.2 The Vibrating String; 5.3 D'Alembert's Solution; 5.4 A Struck String; 5.5 Bernoulli's Solution; 5.6 Time-Independent Problems; 5.7 Time-Dependent Problems; 5.8 Historical Epilogue; Exercises; CHAPTER 6. ORTHOGONAL SYSTEMS; 6.1 Fourier Series and Parseval's Identity; 6.2 An Approximation Problem; 6.3 The Uniform Convergence of Fourier Series; 6.4 Convergence in the Mean; 6.5 Applications to the Vibrating String; 6.6 The Riesz-Fischer Theorem; Exercises CHAPTER 7. FOURIER TRANSFORMS7.1 The Laplace Equation; 7.2 Fourier Transforms; 7.3 Properties of the Fourier Transform; 7.4 Convolution; 7.5 Solution of the Dirichlet Problem for the Half-Plane; 7.6 The Fourier Transform Method; Exercises; CHAPTER 8. LAPLACE TRANSFORMS; 8.1 The Laplace Transform and the Inversion Theorem; 8.2 Properties of the Laplace Transform; 8.3 Convolution; 8.4 The Telegraph Equation; 8.5 The Method of Residues; 8.6 Historical Epilogue; Exercises; CHAPTER 9. BOUNDARY VALUE PROBLEMS IN HIGHER DIMENSIONS; 9.1 Electrostatic Potential in a Charged Box 9.2 Double Fourier Series9.3 The Dirichlet Problem in a Box; 9.4 Return to the Charged Box; 9.5 The Multiple Fourier Transform Method; 9.6 The Double Laplace Transform Method; Exercises; CHAPTER 10. BOUNDARY VALUE PROBLEMS WITH CIRCULAR SYMMETRY; 10.1 Vibrations of a Circular Membrane; 10.2 The Gamma Function; 10.3 Bessel Functions of the First Kind; 10.4 Recursion Formulas for Bessel Functions; 10.5 Bessel Functions of the Second Kind; 10.6 The Zeros of Bessel Functions; 10.7 Orthogonal Systems of Bessel Functions; 10.8 Fourier-Bessel Series and Dini-Bessel Series 10.9 Return to the Vibrating Membrane |
| Record Nr. | UNINA-9910458660803321 |
|
González-Velasco Enrique A
|
||
| San Diego, : Academic Pres, c1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fourier analysis and boundary value problems [[electronic resource] /] / by Enrique A. González-Velasco
| Fourier analysis and boundary value problems [[electronic resource] /] / by Enrique A. González-Velasco |
| Autore | González-Velasco Enrique A |
| Pubbl/distr/stampa | San Diego, : Academic Pres, c1995 |
| Descrizione fisica | 1 online resource (565 p.) |
| Disciplina | 515/.353 |
| Soggetto topico |
Fourier analysis
Boundary value problems - Numerical solutions |
| ISBN |
1-281-03822-9
9786611038229 0-08-053193-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Fourier Analysis and Boundary Value Problems; Copyright Page; Table of Contents; Preface; CHAPTER 1. A HEATED DISCUSSION; 1.1 Historical Prologue; 1.2 The Heat Equation; 1.3 Boundary Value Problems; 1.4 The Method of Separation of Variables; 1.5 Linearity and Superposition of Solutions; 1.6 Historical Epilogue; Exercises; CHAPTER 2. FOURIER SERIES; 2.1 Introduction; 2.2 Fourier Series; 2.3 The Riemann-Lebesgue Theorem; 2.4 The Convergence of Fourier Series; 2.5 Fourier Series on Arbitrary Intervals; 2.6 The Gibbs Phenomenon; 2.7 Fejér Sums; 2.8 Integration of Fourier Series
2.9 Historical EpilogueExercises; CHAPTER 3. RETURN TO THE HEATED BAR; 3.1 Existence of a Solution; 3.2 Uniqueness and Stability of the Solution; 3.3 Nonzero Temperature at the Endpoints; 3.4 Bar Insulated at the Endpoints; 3.5 Mixed Endpoint Conditions; 3.6 Heat Convection at One Endpoint; 3.7 Time-Independent Problems; 3.8 The Steady-State Solution; 3.9 The Transient Solution; 3.10 The Complete Solution; 3.11 Time-Dependent Problems; Exercises; CHAPTER 4. GENERALIZED FOURIER SERIES; 4.1 Sturm-Liouville Problems; 4.2 The Eigenvalues and Eigenfunctions; 4.3 The Existence of the Eigenvalues 4.4 Generalized Fourier Series4.5 Approximations; 4.6 Historical Epilogue; Exercises; CHAPTER 5. THE WAVE EQUATION; 5.1 Introduction; 5.2 The Vibrating String; 5.3 D'Alembert's Solution; 5.4 A Struck String; 5.5 Bernoulli's Solution; 5.6 Time-Independent Problems; 5.7 Time-Dependent Problems; 5.8 Historical Epilogue; Exercises; CHAPTER 6. ORTHOGONAL SYSTEMS; 6.1 Fourier Series and Parseval's Identity; 6.2 An Approximation Problem; 6.3 The Uniform Convergence of Fourier Series; 6.4 Convergence in the Mean; 6.5 Applications to the Vibrating String; 6.6 The Riesz-Fischer Theorem; Exercises CHAPTER 7. FOURIER TRANSFORMS7.1 The Laplace Equation; 7.2 Fourier Transforms; 7.3 Properties of the Fourier Transform; 7.4 Convolution; 7.5 Solution of the Dirichlet Problem for the Half-Plane; 7.6 The Fourier Transform Method; Exercises; CHAPTER 8. LAPLACE TRANSFORMS; 8.1 The Laplace Transform and the Inversion Theorem; 8.2 Properties of the Laplace Transform; 8.3 Convolution; 8.4 The Telegraph Equation; 8.5 The Method of Residues; 8.6 Historical Epilogue; Exercises; CHAPTER 9. BOUNDARY VALUE PROBLEMS IN HIGHER DIMENSIONS; 9.1 Electrostatic Potential in a Charged Box 9.2 Double Fourier Series9.3 The Dirichlet Problem in a Box; 9.4 Return to the Charged Box; 9.5 The Multiple Fourier Transform Method; 9.6 The Double Laplace Transform Method; Exercises; CHAPTER 10. BOUNDARY VALUE PROBLEMS WITH CIRCULAR SYMMETRY; 10.1 Vibrations of a Circular Membrane; 10.2 The Gamma Function; 10.3 Bessel Functions of the First Kind; 10.4 Recursion Formulas for Bessel Functions; 10.5 Bessel Functions of the Second Kind; 10.6 The Zeros of Bessel Functions; 10.7 Orthogonal Systems of Bessel Functions; 10.8 Fourier-Bessel Series and Dini-Bessel Series 10.9 Return to the Vibrating Membrane |
| Record Nr. | UNINA-9910784644503321 |
|
González-Velasco Enrique A
|
||
| San Diego, : Academic Pres, c1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
