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Beginning partial differential equations / / Peter V. O'Neil
| Beginning partial differential equations / / Peter V. O'Neil |
| Autore | O'Neil Peter V. |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (453 p.) |
| Disciplina | 515/.353 |
| Collana | Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts |
| Soggetto topico | Differential equations, Partial |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-118-83210-8 |
| Classificazione | MAT007000 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Beginning Partial Differential Equations; Copyright; Contents; Preface; 1 First Ideas; 1.1 Two Partial Differential Equations; 1.1.1 The Heat, or Diffusion, Equati; 1.1.2 The Wave Equation; 1.2 Fourier Series; 1.2.1 The Fourier Series of a Function; 1.2.2 Fourier Sine and Cosine Series; 1.3 Two Eigenvalue Problems; 1.4 A Proof of the Fourier Convergence Theorem; 1.4.1 The Role of Periodicity; 1.4.2 Dirichlet's Formula; 1.4.3 The Riemann-Lebesgue Lemma; 1.4.4 Proof of the Convergence Theorem; 2 Solutions of the Heat Equation; 2.1 Solutions on an Interval [0, L]
2.1.1 Ends Kept at Temperature Zero2.1.2 Insulated Ends; 2.1.3 Ends at Different Temperatures; 2.1.4 A Diffusion Equation with Additional Terms; 2.1.5 One Radiating End; 2.2 A Nonhomogeneous Problem; 2.3 The Heat Equation in Two Space Variables; 2.4 The Weak Maximum Principle; 3 Solutions of the Wave Equation; 3.1 Solutions on Bounded Intervals; 3.1.1 Fixed Ends; 3.1.2 Fixed Ends with a Forcing Term; 3.1.3 Damped Wave Motion; 3.2 The Cauchy Problem; 3.2.1 d'Alembert's Solution; 3.2.1.1 Forward and Backward Waves; 3.2.2 The Cauchy Problem on a Half Line 3.2.3 Characteristic Triangles and Quadrilaterals3.2.4 A Cauchy Problem with a Forcing Term; 3.2.5 String with Moving Ends; 3.3 The Wave Equation in Higher Dimensions; 3.3.1 Vibrations in a Membrane with Fixed Frame; 3.3.2 The Poisson Integral Solution; 3.3.3 Hadamard's Method of Descent; 4 Dirichlet and Neumann Problems; 4.1 Laplace's Equation and Harmonic Functions; 4.1.1 Laplace's Equation in Polar Coordinates; 4.1.2 Laplace's Equation in Three Dimensions; 4.2 The Dirichlet Problem for a Rectangle; 4.3 The Dirichlet Problem for a Disk; 4.3.1 Poisson's Integral Solution 4.4 Properties of Harmonic Functions4.4.1 Topology of Rn; 4.4.2 Representation Theorems; 4.4.2.1 A Representation Theorem in R3; 4.4.2.2 A Representation Theorem in the Plane; 4.4.3 The Mean Value Property and the Maximum Principle; 4.5 The Neumann Problem; 4.5.1 Existence and Uniqueness; 4.5.2 Neumann Problem for a Rectangle; 4.5.3 Neumann Problem for a Disk; 4.6 Poisson's Equation; 4. 7 Existence Theorem for a Dirichlet Problem; 5 Fourier Integral Methods of Solution; 5.1 The Fourier Integral of a Function; 5.1.1 Fourier Cosine and Sine Integrals; 5.2 The Heat Equation on the Real Line 5.2.1 A Reformulation of the Integral Solution5.2.2 The Heat Equation on a Half Line; 5.3 The Debate over the Age of the Earth; 5.4 Burger's Equation; 5.4.1 Traveling Wave Solutions of Burger's Equation; 5.5 The Cauchy Problem for the Wave Equation; 5.6 Laplace's Equation on Unbounded Domains; 5.6.1 Dirichlet Problem for the Upper Half Plane; 5.6.2 Dirichlet Problem for the Right Quarter Plane; 5.6.3 A Neumann Problem for the Upper Half Plane; 6 Solutions Using Eigenfunction Expansions; 6.1 A Theory of Eigenfunction Expansions; 6.1.1 A Closer Look at Expansion Coefficients 6.2 Bessel Functions |
| Record Nr. | UNINA-9910458529203321 |
O'Neil Peter V.
|
||
| Hoboken, New Jersey : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Beginning partial differential equations / / Peter V. O'Neil
| Beginning partial differential equations / / Peter V. O'Neil |
| Autore | O'Neil Peter V. |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (453 p.) |
| Disciplina | 515/.353 |
| Collana | Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts |
| Soggetto topico | Differential equations, Partial |
| ISBN | 1-118-83210-8 |
| Classificazione | MAT007000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Beginning Partial Differential Equations; Copyright; Contents; Preface; 1 First Ideas; 1.1 Two Partial Differential Equations; 1.1.1 The Heat, or Diffusion, Equati; 1.1.2 The Wave Equation; 1.2 Fourier Series; 1.2.1 The Fourier Series of a Function; 1.2.2 Fourier Sine and Cosine Series; 1.3 Two Eigenvalue Problems; 1.4 A Proof of the Fourier Convergence Theorem; 1.4.1 The Role of Periodicity; 1.4.2 Dirichlet's Formula; 1.4.3 The Riemann-Lebesgue Lemma; 1.4.4 Proof of the Convergence Theorem; 2 Solutions of the Heat Equation; 2.1 Solutions on an Interval [0, L]
2.1.1 Ends Kept at Temperature Zero2.1.2 Insulated Ends; 2.1.3 Ends at Different Temperatures; 2.1.4 A Diffusion Equation with Additional Terms; 2.1.5 One Radiating End; 2.2 A Nonhomogeneous Problem; 2.3 The Heat Equation in Two Space Variables; 2.4 The Weak Maximum Principle; 3 Solutions of the Wave Equation; 3.1 Solutions on Bounded Intervals; 3.1.1 Fixed Ends; 3.1.2 Fixed Ends with a Forcing Term; 3.1.3 Damped Wave Motion; 3.2 The Cauchy Problem; 3.2.1 d'Alembert's Solution; 3.2.1.1 Forward and Backward Waves; 3.2.2 The Cauchy Problem on a Half Line 3.2.3 Characteristic Triangles and Quadrilaterals3.2.4 A Cauchy Problem with a Forcing Term; 3.2.5 String with Moving Ends; 3.3 The Wave Equation in Higher Dimensions; 3.3.1 Vibrations in a Membrane with Fixed Frame; 3.3.2 The Poisson Integral Solution; 3.3.3 Hadamard's Method of Descent; 4 Dirichlet and Neumann Problems; 4.1 Laplace's Equation and Harmonic Functions; 4.1.1 Laplace's Equation in Polar Coordinates; 4.1.2 Laplace's Equation in Three Dimensions; 4.2 The Dirichlet Problem for a Rectangle; 4.3 The Dirichlet Problem for a Disk; 4.3.1 Poisson's Integral Solution 4.4 Properties of Harmonic Functions4.4.1 Topology of Rn; 4.4.2 Representation Theorems; 4.4.2.1 A Representation Theorem in R3; 4.4.2.2 A Representation Theorem in the Plane; 4.4.3 The Mean Value Property and the Maximum Principle; 4.5 The Neumann Problem; 4.5.1 Existence and Uniqueness; 4.5.2 Neumann Problem for a Rectangle; 4.5.3 Neumann Problem for a Disk; 4.6 Poisson's Equation; 4. 7 Existence Theorem for a Dirichlet Problem; 5 Fourier Integral Methods of Solution; 5.1 The Fourier Integral of a Function; 5.1.1 Fourier Cosine and Sine Integrals; 5.2 The Heat Equation on the Real Line 5.2.1 A Reformulation of the Integral Solution5.2.2 The Heat Equation on a Half Line; 5.3 The Debate over the Age of the Earth; 5.4 Burger's Equation; 5.4.1 Traveling Wave Solutions of Burger's Equation; 5.5 The Cauchy Problem for the Wave Equation; 5.6 Laplace's Equation on Unbounded Domains; 5.6.1 Dirichlet Problem for the Upper Half Plane; 5.6.2 Dirichlet Problem for the Right Quarter Plane; 5.6.3 A Neumann Problem for the Upper Half Plane; 6 Solutions Using Eigenfunction Expansions; 6.1 A Theory of Eigenfunction Expansions; 6.1.1 A Closer Look at Expansion Coefficients 6.2 Bessel Functions |
| Record Nr. | UNINA-9910791029003321 |
|
O'Neil Peter V.
|
||
| Hoboken, New Jersey : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Beginning partial differential equations / / Peter V. O'Neil
| Beginning partial differential equations / / Peter V. O'Neil |
| Autore | O'Neil Peter V. |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (453 p.) |
| Disciplina | 515/.353 |
| Collana | Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts |
| Soggetto topico | Differential equations, Partial |
| ISBN | 1-118-83210-8 |
| Classificazione | MAT007000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Beginning Partial Differential Equations; Copyright; Contents; Preface; 1 First Ideas; 1.1 Two Partial Differential Equations; 1.1.1 The Heat, or Diffusion, Equati; 1.1.2 The Wave Equation; 1.2 Fourier Series; 1.2.1 The Fourier Series of a Function; 1.2.2 Fourier Sine and Cosine Series; 1.3 Two Eigenvalue Problems; 1.4 A Proof of the Fourier Convergence Theorem; 1.4.1 The Role of Periodicity; 1.4.2 Dirichlet's Formula; 1.4.3 The Riemann-Lebesgue Lemma; 1.4.4 Proof of the Convergence Theorem; 2 Solutions of the Heat Equation; 2.1 Solutions on an Interval [0, L]
2.1.1 Ends Kept at Temperature Zero2.1.2 Insulated Ends; 2.1.3 Ends at Different Temperatures; 2.1.4 A Diffusion Equation with Additional Terms; 2.1.5 One Radiating End; 2.2 A Nonhomogeneous Problem; 2.3 The Heat Equation in Two Space Variables; 2.4 The Weak Maximum Principle; 3 Solutions of the Wave Equation; 3.1 Solutions on Bounded Intervals; 3.1.1 Fixed Ends; 3.1.2 Fixed Ends with a Forcing Term; 3.1.3 Damped Wave Motion; 3.2 The Cauchy Problem; 3.2.1 d'Alembert's Solution; 3.2.1.1 Forward and Backward Waves; 3.2.2 The Cauchy Problem on a Half Line 3.2.3 Characteristic Triangles and Quadrilaterals3.2.4 A Cauchy Problem with a Forcing Term; 3.2.5 String with Moving Ends; 3.3 The Wave Equation in Higher Dimensions; 3.3.1 Vibrations in a Membrane with Fixed Frame; 3.3.2 The Poisson Integral Solution; 3.3.3 Hadamard's Method of Descent; 4 Dirichlet and Neumann Problems; 4.1 Laplace's Equation and Harmonic Functions; 4.1.1 Laplace's Equation in Polar Coordinates; 4.1.2 Laplace's Equation in Three Dimensions; 4.2 The Dirichlet Problem for a Rectangle; 4.3 The Dirichlet Problem for a Disk; 4.3.1 Poisson's Integral Solution 4.4 Properties of Harmonic Functions4.4.1 Topology of Rn; 4.4.2 Representation Theorems; 4.4.2.1 A Representation Theorem in R3; 4.4.2.2 A Representation Theorem in the Plane; 4.4.3 The Mean Value Property and the Maximum Principle; 4.5 The Neumann Problem; 4.5.1 Existence and Uniqueness; 4.5.2 Neumann Problem for a Rectangle; 4.5.3 Neumann Problem for a Disk; 4.6 Poisson's Equation; 4. 7 Existence Theorem for a Dirichlet Problem; 5 Fourier Integral Methods of Solution; 5.1 The Fourier Integral of a Function; 5.1.1 Fourier Cosine and Sine Integrals; 5.2 The Heat Equation on the Real Line 5.2.1 A Reformulation of the Integral Solution5.2.2 The Heat Equation on a Half Line; 5.3 The Debate over the Age of the Earth; 5.4 Burger's Equation; 5.4.1 Traveling Wave Solutions of Burger's Equation; 5.5 The Cauchy Problem for the Wave Equation; 5.6 Laplace's Equation on Unbounded Domains; 5.6.1 Dirichlet Problem for the Upper Half Plane; 5.6.2 Dirichlet Problem for the Right Quarter Plane; 5.6.3 A Neumann Problem for the Upper Half Plane; 6 Solutions Using Eigenfunction Expansions; 6.1 A Theory of Eigenfunction Expansions; 6.1.1 A Closer Look at Expansion Coefficients 6.2 Bessel Functions |
| Record Nr. | UNINA-9910814815703321 |
|
O'Neil Peter V.
|
||
| Hoboken, New Jersey : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Solutions manual for beginning partial differential equations / / Peter V. O'Neil
| Solutions manual for beginning partial differential equations / / Peter V. O'Neil |
| Autore | O'Neil Peter V. |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (199 p.) |
| Disciplina | 515.35076 |
| Collana | Pure and Applied Mathematics : A Wiley Series of Texts, Monographs and Tracts |
| Soggetto topico | Differential equations |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-88058-7
1-118-62998-1 1-118-96967-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Series; Title Page; Copyright; Preface; Chapter 1: First Ideas; 1.1 Two Partial Differential Equations; 1.2 Fourier Series; 1.3 Two Eigenvalue Problems; 1.4 A Proof of the Convergence Theorem; Chapter 2: Solutions of the Heat Equation; 2.1 Solutions on an Interval [0,L]; 2.2 A Nonhomogeneous Problem; Chapter 3: Solutions of the Wave Equation; 3.1 Solutions on Bounded Intervals; 3.2 The Cauchy Problem; 3.3 The Wave Equation in Higher Dimensions; Chapter 4: Dirichlet and Neumann Problems; 4.1 Laplace''s Equation and Harmonic Functions; 4.2 The Dirichlet Problem for a Rectangle
4.3 The Dirichlet Problem for a Disk4.4 Properties of Harmonic Functions; 4.5 The Neumann Problem; 4.6 Poisson''s Equation; 4.7 An Existence Theorem for the Dirichlet Problem; Chapter 5: Fourier Integral Methods of Solution; 5.1 The Fourier Integral of a Function; 5.2 The Heat Equation on the Real Line; 5.3 The Debate Over the Age of the Earth; 5.4 Burgers' Equation; 5.5 The Cauchy Problem for the Wave Equation; 5.6 Laplace''s Equation on Unbounded Domains; Chapter 6: Solutions Using Eigenfunction Expansions; 6.1 A Theory of Eigenfunction Expansions; 6.2 Bessel Functions 6.3 Applications of Bessel Functions6.4 Legendre Polynomials and Applications; Chapter 7: Integral Transform Methods of Solution; 7.1 The Fourier Transform; 7.2 Heat and Wave Equations; 7.3 The Telegraph Equation; 7.4 The Laplace Transform; Chapter 8: First-Order Equations; 8.1 Linear First-Order Equations; 8.2 The Significance of Characteristics; 8.3 The Quasi-Linear Equation; Series List; End User License Agreement |
| Record Nr. | UNINA-9910460076103321 |
|
O'Neil Peter V.
|
||
| Hoboken, New Jersey : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Solutions manual for beginning partial differential equations / / Peter V. O'Neil
| Solutions manual for beginning partial differential equations / / Peter V. O'Neil |
| Autore | O'Neil Peter V. |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (199 p.) |
| Disciplina | 515.35076 |
| Collana | Pure and Applied Mathematics : A Wiley Series of Texts, Monographs and Tracts |
| Soggetto topico | Differential equations |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-88058-7
1-118-62998-1 1-118-96967-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Series; Title Page; Copyright; Preface; Chapter 1: First Ideas; 1.1 Two Partial Differential Equations; 1.2 Fourier Series; 1.3 Two Eigenvalue Problems; 1.4 A Proof of the Convergence Theorem; Chapter 2: Solutions of the Heat Equation; 2.1 Solutions on an Interval [0,L]; 2.2 A Nonhomogeneous Problem; Chapter 3: Solutions of the Wave Equation; 3.1 Solutions on Bounded Intervals; 3.2 The Cauchy Problem; 3.3 The Wave Equation in Higher Dimensions; Chapter 4: Dirichlet and Neumann Problems; 4.1 Laplace''s Equation and Harmonic Functions; 4.2 The Dirichlet Problem for a Rectangle
4.3 The Dirichlet Problem for a Disk4.4 Properties of Harmonic Functions; 4.5 The Neumann Problem; 4.6 Poisson''s Equation; 4.7 An Existence Theorem for the Dirichlet Problem; Chapter 5: Fourier Integral Methods of Solution; 5.1 The Fourier Integral of a Function; 5.2 The Heat Equation on the Real Line; 5.3 The Debate Over the Age of the Earth; 5.4 Burgers' Equation; 5.5 The Cauchy Problem for the Wave Equation; 5.6 Laplace''s Equation on Unbounded Domains; Chapter 6: Solutions Using Eigenfunction Expansions; 6.1 A Theory of Eigenfunction Expansions; 6.2 Bessel Functions 6.3 Applications of Bessel Functions6.4 Legendre Polynomials and Applications; Chapter 7: Integral Transform Methods of Solution; 7.1 The Fourier Transform; 7.2 Heat and Wave Equations; 7.3 The Telegraph Equation; 7.4 The Laplace Transform; Chapter 8: First-Order Equations; 8.1 Linear First-Order Equations; 8.2 The Significance of Characteristics; 8.3 The Quasi-Linear Equation; Series List; End User License Agreement |
| Record Nr. | UNINA-9910595381803321 |
|
O'Neil Peter V.
|
||
| Hoboken, New Jersey : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||