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Analytic Methods for Partial Differential Equations [[electronic resource] /] / by G. Evans, J. Blackledge, P. Yardley
| Analytic Methods for Partial Differential Equations [[electronic resource] /] / by G. Evans, J. Blackledge, P. Yardley |
| Autore | Evans G |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | London : , : Springer London : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (XII, 316 p.) |
| Disciplina | 515/.353 |
| Collana | Springer Undergraduate Mathematics Series |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Numerical analysis Analysis Numerical Analysis |
| ISBN | 1-4471-0379-3 |
| Classificazione |
35C15
35A22 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Mathematical Preliminaries -- 1.1 Introduction -- 1.2 Characteristics and Classification -- 1.3 Orthogonal Functions -- 1.4 Sturm-Liouville Boundary Value Problems -- 1.5 Legendre Polynomials -- 1.6 Bessel Functions -- 1.7 Results from Complex Analysis -- 1.8 Generalised Functions and the Delta Function -- 2. Separation of the Variables -- 2.1 Introduction -- 2.2 The Wave Equation -- 2.3 The Heat Equation -- 2.4 Laplace’s Equation -- 2.5 Homogeneous and Non-homogeneous Boundary Conditions -- 2.6 Separation of variables in other coordinate systems -- 3. First-order Equations and Hyperbolic Second-order Equations -- 3.1 Introduction -- 3.2 First-order equations -- 3.3 Introduction to d’Alembert’s Method -- 3.4 d’Alembert’s General Solution -- 3.5 Characteristics -- 3.6 Semi-infinite Strings -- 4. Integral Transforms -- 4.1 Introduction -- 4.2 Fourier Integrals -- 4.3 Application to the Heat Equation -- 4.4 Fourier Sine and Cosine Transforms -- 4.5 General Fourier Transforms -- 4.6 Laplace transform -- 4.7 Inverting Laplace Transforms -- 4.8 Standard Transforms -- 4.9 Use of Laplace Transforms to Solve Partial Differential Equations -- 5. Green’s Functions -- 5.1 Introduction -- 5.2 Green’s Functions for the Time-independent Wave Equation -- 5.3 Green’s Function Solution to the Three-dimensional Inhomogeneous Wave Equation -- 5.4 Green’s Function Solutions to the Inhomogeneous Helmholtz and Schrödinger Equations: An Introduction to Scattering Theory -- 5.5 Green’s Function Solution to Maxwell’s Equations and Time-dependent Problems -- 5.6 Green’s Functions and Optics: Kirchhoff Diffraction Theory -- 5.7 Approximation Methods and the Born Series -- 5.8 Green’s Function Solution to the Diffusion Equation -- 5.9 Green’s Function Solution to the Laplace and Poisson Equations -- 5.10 Discussion -- A. Solutions of Exercises. |
| Record Nr. | UNINA-9910479882503321 |
Evans G
|
||
| London : , : Springer London : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Analytic Methods for Partial Differential Equations [[electronic resource] /] / by G. Evans, J. Blackledge, P. Yardley
| Analytic Methods for Partial Differential Equations [[electronic resource] /] / by G. Evans, J. Blackledge, P. Yardley |
| Autore | Evans G |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | London : , : Springer London : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (XII, 316 p.) |
| Disciplina | 515/.353 |
| Collana | Springer Undergraduate Mathematics Series |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Numerical analysis Analysis Numerical Analysis |
| ISBN | 1-4471-0379-3 |
| Classificazione |
35C15
35A22 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Mathematical Preliminaries -- 1.1 Introduction -- 1.2 Characteristics and Classification -- 1.3 Orthogonal Functions -- 1.4 Sturm-Liouville Boundary Value Problems -- 1.5 Legendre Polynomials -- 1.6 Bessel Functions -- 1.7 Results from Complex Analysis -- 1.8 Generalised Functions and the Delta Function -- 2. Separation of the Variables -- 2.1 Introduction -- 2.2 The Wave Equation -- 2.3 The Heat Equation -- 2.4 Laplace’s Equation -- 2.5 Homogeneous and Non-homogeneous Boundary Conditions -- 2.6 Separation of variables in other coordinate systems -- 3. First-order Equations and Hyperbolic Second-order Equations -- 3.1 Introduction -- 3.2 First-order equations -- 3.3 Introduction to d’Alembert’s Method -- 3.4 d’Alembert’s General Solution -- 3.5 Characteristics -- 3.6 Semi-infinite Strings -- 4. Integral Transforms -- 4.1 Introduction -- 4.2 Fourier Integrals -- 4.3 Application to the Heat Equation -- 4.4 Fourier Sine and Cosine Transforms -- 4.5 General Fourier Transforms -- 4.6 Laplace transform -- 4.7 Inverting Laplace Transforms -- 4.8 Standard Transforms -- 4.9 Use of Laplace Transforms to Solve Partial Differential Equations -- 5. Green’s Functions -- 5.1 Introduction -- 5.2 Green’s Functions for the Time-independent Wave Equation -- 5.3 Green’s Function Solution to the Three-dimensional Inhomogeneous Wave Equation -- 5.4 Green’s Function Solutions to the Inhomogeneous Helmholtz and Schrödinger Equations: An Introduction to Scattering Theory -- 5.5 Green’s Function Solution to Maxwell’s Equations and Time-dependent Problems -- 5.6 Green’s Functions and Optics: Kirchhoff Diffraction Theory -- 5.7 Approximation Methods and the Born Series -- 5.8 Green’s Function Solution to the Diffusion Equation -- 5.9 Green’s Function Solution to the Laplace and Poisson Equations -- 5.10 Discussion -- A. Solutions of Exercises. |
| Record Nr. | UNINA-9910789350903321 |
|
Evans G
|
||
| London : , : Springer London : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Analytic Methods for Partial Differential Equations [[electronic resource] /] / by G. Evans, J. Blackledge, P. Yardley
| Analytic Methods for Partial Differential Equations [[electronic resource] /] / by G. Evans, J. Blackledge, P. Yardley |
| Autore | Evans G |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | London : , : Springer London : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (XII, 316 p.) |
| Disciplina | 515/.353 |
| Collana | Springer Undergraduate Mathematics Series |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Numerical analysis Analysis Numerical Analysis |
| ISBN | 1-4471-0379-3 |
| Classificazione |
35C15
35A22 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Mathematical Preliminaries -- 1.1 Introduction -- 1.2 Characteristics and Classification -- 1.3 Orthogonal Functions -- 1.4 Sturm-Liouville Boundary Value Problems -- 1.5 Legendre Polynomials -- 1.6 Bessel Functions -- 1.7 Results from Complex Analysis -- 1.8 Generalised Functions and the Delta Function -- 2. Separation of the Variables -- 2.1 Introduction -- 2.2 The Wave Equation -- 2.3 The Heat Equation -- 2.4 Laplace’s Equation -- 2.5 Homogeneous and Non-homogeneous Boundary Conditions -- 2.6 Separation of variables in other coordinate systems -- 3. First-order Equations and Hyperbolic Second-order Equations -- 3.1 Introduction -- 3.2 First-order equations -- 3.3 Introduction to d’Alembert’s Method -- 3.4 d’Alembert’s General Solution -- 3.5 Characteristics -- 3.6 Semi-infinite Strings -- 4. Integral Transforms -- 4.1 Introduction -- 4.2 Fourier Integrals -- 4.3 Application to the Heat Equation -- 4.4 Fourier Sine and Cosine Transforms -- 4.5 General Fourier Transforms -- 4.6 Laplace transform -- 4.7 Inverting Laplace Transforms -- 4.8 Standard Transforms -- 4.9 Use of Laplace Transforms to Solve Partial Differential Equations -- 5. Green’s Functions -- 5.1 Introduction -- 5.2 Green’s Functions for the Time-independent Wave Equation -- 5.3 Green’s Function Solution to the Three-dimensional Inhomogeneous Wave Equation -- 5.4 Green’s Function Solutions to the Inhomogeneous Helmholtz and Schrödinger Equations: An Introduction to Scattering Theory -- 5.5 Green’s Function Solution to Maxwell’s Equations and Time-dependent Problems -- 5.6 Green’s Functions and Optics: Kirchhoff Diffraction Theory -- 5.7 Approximation Methods and the Born Series -- 5.8 Green’s Function Solution to the Diffusion Equation -- 5.9 Green’s Function Solution to the Laplace and Poisson Equations -- 5.10 Discussion -- A. Solutions of Exercises. |
| Record Nr. | UNINA-9910827669903321 |
|
Evans G
|
||
| London : , : Springer London : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||