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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-> |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2012 |
| Descrizione fisica | 1 online resource (694 p.) |
| Disciplina | 515/.353 |
| Soggetto topico | Differential equations, Partial |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-118-44146-X |
| 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-9910465463003321 |
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-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 | ||
| ||