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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 | ||
| ||
Nonlinear Perron-Frobenius theory / / Bas Lemmens, Roger Nussbaum [[electronic resource]]
| Nonlinear Perron-Frobenius theory / / Bas Lemmens, Roger Nussbaum [[electronic resource]] |
| Autore | Lemmens Bas |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2012 |
| Descrizione fisica | 1 online resource (xii, 323 pages) : digital, PDF file(s) |
| Disciplina | 512/.5 |
| Collana | Cambridge tracts in mathematics |
| Soggetto topico |
Non-negative matrices
Eigenvalues Eigenvectors Algebras, Linear |
| ISBN |
1-107-22634-1
1-280-87795-2 9786613719263 1-139-37825-2 1-139-02607-0 1-139-37539-3 1-139-37140-1 1-139-37968-2 1-139-37682-9 |
| Classificazione | MAT007000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- What is nonlinear Perron-Frobenius theory? -- Non-expansiveness and nonlinear Perron-Frobenius theory -- Dynamics of non-expansive maps -- Sup-norm non-expansive maps -- Eigenvectors and eigenvalues of nonlinear cone maps -- Eigenvectors in the interior of the cone -- Applications to matrix scaling problems -- Dynamics of subhomogeneous maps -- Dynamics of integral-preserving maps -- Appendix A. The Birkhoff-Hopf theorem -- Appendix B. Classical Perron-Frobenius theory. |
| Record Nr. | UNINA-9910790305303321 |
|
Lemmens Bas
|
||
| Cambridge : , : Cambridge University Press, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear Perron-Frobenius theory / / Bas Lemmens, Roger Nussbaum [[electronic resource]]
| Nonlinear Perron-Frobenius theory / / Bas Lemmens, Roger Nussbaum [[electronic resource]] |
| Autore | Lemmens Bas |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2012 |
| Descrizione fisica | 1 online resource (xii, 323 pages) : digital, PDF file(s) |
| Disciplina | 512/.5 |
| Collana | Cambridge tracts in mathematics |
| Soggetto topico |
Non-negative matrices
Eigenvalues Eigenvectors Algebras, Linear |
| ISBN |
1-107-22634-1
1-280-87795-2 9786613719263 1-139-37825-2 1-139-02607-0 1-139-37539-3 1-139-37140-1 1-139-37968-2 1-139-37682-9 |
| Classificazione | MAT007000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- What is nonlinear Perron-Frobenius theory? -- Non-expansiveness and nonlinear Perron-Frobenius theory -- Dynamics of non-expansive maps -- Sup-norm non-expansive maps -- Eigenvectors and eigenvalues of nonlinear cone maps -- Eigenvectors in the interior of the cone -- Applications to matrix scaling problems -- Dynamics of subhomogeneous maps -- Dynamics of integral-preserving maps -- Appendix A. The Birkhoff-Hopf theorem -- Appendix B. Classical Perron-Frobenius theory. |
| Record Nr. | UNINA-9910809659603321 |
|
Lemmens Bas
|
||
| Cambridge : , : Cambridge University Press, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Partial differential equations : theory and completely solved problems / / Thomas Hillen, I. Ed Leonard, Henry van Roessel
| Partial differential equations : theory and completely solved problems / / Thomas Hillen, I. Ed Leonard, Henry van Roessel |
| Autore | Hillen Thomas <1966-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2012 |
| Descrizione fisica | 1 online resource (694 p.) |
| Disciplina | 515/.353 |
| Soggetto topico | Differential equations, Partial |
| ISBN | 1-118-44146-X |
| Classificazione | MAT007000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page ; Copyright; Contents ; Preface ; PART I: THEORY ; Chapter 1: Introduction ; 1.1 Partial Differential Equations ; 11.2 Classification of Second-order Linear Pdes ; 1.3 Side Conditions ; 1.3.1 Boundary Conditions on an Interval ; 1.4 Linear Pdes ; 1.4.1 Principle of Superposition ; 1.5 Steady-state and Equilibrium Solutions ; 1.6 First Example for Separation of Variables ; 1.7 Derivation of the Diffusion Equation ; 1.7.1 Boundary Conditions ; 1.8 Derivation of the Heat Equation ; 1.9 Derivation of the Wave Equation ; 1.10 Examples of Laplace''s Equation ; 1.11 Summary
1.11.1 Problems and Notes Chapter 2: Fourier Series ; 2.1 Piecewise Continuous Functions ; 2.2 Even, Odd, and Periodic Functions ; 2.3 Orthogonal Functions ; 2.4 Fourier Series ; 2.4.1 Fourier Sine and Cosine Series ; 2.5 Convergence of Fourier Series ; 2.5.1 Gibbs'' Phenomenon ; 2.6 Operations on Fourier Series ; 2.7 Mean Square Error ; 2.8 Complex Fourier Series ; 2.9 Summary ; 2.9.1 Problems and Notes ; Chapter 3: Separation of Variables ; 3.1 Homogeneous Equations ; 3.1.1 General Linear Homogeneous Equations ; 3.1.2 Limitations of the Method of Separation of Variables 3.2 Nonhomogeneous Equations 3.2.1 Method of Eigenfunction Expansions ; 3.3 Summary ; 3.3.1 Problems and Notes ; Chapter 4: Sturm Liouville Theory ; 4.1 Formulation ; 4.2 Properties of Sturm-liouville Problems ; 4.3 Eigenfunction Expansions ; 4.4 Rayleigh Quotient ; 4.5 Summary ; 4.5.1 Problems and Notes ; Chapter 5: Heat, Wave, and Laplace Equations ; 5.1 One-dimensional Heat Equation ; 5.2 Two-dimensional Heat Equation ; 5.3 One-dimensional Wave Equation ; 5.3.1 d'' Alembert''s Solution ; 5.4 Laplace''s Equation ; 5.4.1 Potential in a Rectangle ; 5.5 Maximum Principle 5.6 Two-dimensional Wave Equation 5.7 Eigenfunctions in Two Dimensions ; 5.8 Summary ; 5.8.1 Problems and Notes ; Chapter 6: Polar Coordinates ; 6.1 Interior Dirichlet Problem for a Disk ; 6.1.1 Poisson Integral Formula ; 6.2 Vibrating Circular Membrane ; 6.3 Bessel''s Equation ; 6.3.1 Series Solutions of Odes ; 6.4 Bessel Functions ; 6.4.1 Properties of Bessel Functions ; 6.4.2 Integral Representation of Bessel Functions ; 6.5 Fourier-bessel Series ; 6.6 Solution to the Vibrating Membrane Problem ; 6.7 Summary ; 6.7.1 Problems and Notes ; Chapter 7: Spherical Coordinates 7.1 Spherical Coordinates 7.1.1 Derivation of the Laplacian ; 7.2 Legendre''s Equation ; 7.3 Legendre Functions ; 7.3.1 Legendre Polynomials ; 7.3.2 Fourier-legendre Series ; 7.3.3 Legendre Functions of the Second Kind ; 7.3.4 Associated Legendre Functions ; 7.4 Spherical Bessel Functions ; 7.5 Interior Dirichlet Problem for a Sphere ; 7.6 Summary ; 7.6.1 Problems and Notes ; Chapter 8: Fourier Transforms ; 8.1 Fourier Integrals ; 8.1.1 Fourier Integral Representation ; 8.1.2 Examples ; 8.1.3 Fourier Sine and Cosine Integral Representations ; 8.1.4 Proof of Fourier''s Theorem 8.2 Fourier Transforms |
| Record Nr. | UNINA-9910787091703321 |
|
Hillen Thomas <1966->
|
||
| Hoboken, New Jersey : , : Wiley, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Partial differential equations : theory and completely solved problems / / Thomas Hillen, I. Ed Leonard, Henry van Roessel
| Partial differential equations : theory and completely solved problems / / Thomas Hillen, I. Ed Leonard, Henry van Roessel |
| Autore | Hillen Thomas <1966-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2012 |
| Descrizione fisica | 1 online resource (694 p.) |
| Disciplina | 515/.353 |
| Soggetto topico | Differential equations, Partial |
| ISBN | 1-118-44146-X |
| Classificazione | MAT007000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page ; Copyright; Contents ; Preface ; PART I: THEORY ; Chapter 1: Introduction ; 1.1 Partial Differential Equations ; 11.2 Classification of Second-order Linear Pdes ; 1.3 Side Conditions ; 1.3.1 Boundary Conditions on an Interval ; 1.4 Linear Pdes ; 1.4.1 Principle of Superposition ; 1.5 Steady-state and Equilibrium Solutions ; 1.6 First Example for Separation of Variables ; 1.7 Derivation of the Diffusion Equation ; 1.7.1 Boundary Conditions ; 1.8 Derivation of the Heat Equation ; 1.9 Derivation of the Wave Equation ; 1.10 Examples of Laplace''s Equation ; 1.11 Summary
1.11.1 Problems and Notes Chapter 2: Fourier Series ; 2.1 Piecewise Continuous Functions ; 2.2 Even, Odd, and Periodic Functions ; 2.3 Orthogonal Functions ; 2.4 Fourier Series ; 2.4.1 Fourier Sine and Cosine Series ; 2.5 Convergence of Fourier Series ; 2.5.1 Gibbs'' Phenomenon ; 2.6 Operations on Fourier Series ; 2.7 Mean Square Error ; 2.8 Complex Fourier Series ; 2.9 Summary ; 2.9.1 Problems and Notes ; Chapter 3: Separation of Variables ; 3.1 Homogeneous Equations ; 3.1.1 General Linear Homogeneous Equations ; 3.1.2 Limitations of the Method of Separation of Variables 3.2 Nonhomogeneous Equations 3.2.1 Method of Eigenfunction Expansions ; 3.3 Summary ; 3.3.1 Problems and Notes ; Chapter 4: Sturm Liouville Theory ; 4.1 Formulation ; 4.2 Properties of Sturm-liouville Problems ; 4.3 Eigenfunction Expansions ; 4.4 Rayleigh Quotient ; 4.5 Summary ; 4.5.1 Problems and Notes ; Chapter 5: Heat, Wave, and Laplace Equations ; 5.1 One-dimensional Heat Equation ; 5.2 Two-dimensional Heat Equation ; 5.3 One-dimensional Wave Equation ; 5.3.1 d'' Alembert''s Solution ; 5.4 Laplace''s Equation ; 5.4.1 Potential in a Rectangle ; 5.5 Maximum Principle 5.6 Two-dimensional Wave Equation 5.7 Eigenfunctions in Two Dimensions ; 5.8 Summary ; 5.8.1 Problems and Notes ; Chapter 6: Polar Coordinates ; 6.1 Interior Dirichlet Problem for a Disk ; 6.1.1 Poisson Integral Formula ; 6.2 Vibrating Circular Membrane ; 6.3 Bessel''s Equation ; 6.3.1 Series Solutions of Odes ; 6.4 Bessel Functions ; 6.4.1 Properties of Bessel Functions ; 6.4.2 Integral Representation of Bessel Functions ; 6.5 Fourier-bessel Series ; 6.6 Solution to the Vibrating Membrane Problem ; 6.7 Summary ; 6.7.1 Problems and Notes ; Chapter 7: Spherical Coordinates 7.1 Spherical Coordinates 7.1.1 Derivation of the Laplacian ; 7.2 Legendre''s Equation ; 7.3 Legendre Functions ; 7.3.1 Legendre Polynomials ; 7.3.2 Fourier-legendre Series ; 7.3.3 Legendre Functions of the Second Kind ; 7.3.4 Associated Legendre Functions ; 7.4 Spherical Bessel Functions ; 7.5 Interior Dirichlet Problem for a Sphere ; 7.6 Summary ; 7.6.1 Problems and Notes ; Chapter 8: Fourier Transforms ; 8.1 Fourier Integrals ; 8.1.1 Fourier Integral Representation ; 8.1.2 Examples ; 8.1.3 Fourier Sine and Cosine Integral Representations ; 8.1.4 Proof of Fourier''s Theorem 8.2 Fourier Transforms |
| Record Nr. | UNINA-9910819250603321 |
|
Hillen Thomas <1966->
|
||
| Hoboken, New Jersey : , : Wiley, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||