Boundary Value Problems for Linear Partial Differential Equations
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Boundary Value Problems for Linear Partial Differential Equations
Manas, Manuel; Alonso, Luis Martinez
Taylor & Francis Ltd
06/2024
456
Dura
9781032662527
Pré-lançamento - envio 15 a 20 dias após a sua edição
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1. Introduction. 1.1. Partial Differential Equations. 1.2. Boundary and Initial Conditions. 1.3. Local Solvability. 1.4. Characteristics. 1.5. General Solutions. 1.6. Remarkable Lives and Achievements. 2. Linear PDEs. 2.1. Linear Differential Operators. 2.2. 1D Eigenvalue Problems. 2.3. Linear BVPs in Physics. 2.4. Exercises. 3. Separation of Variables Method. 3.1. Separable Homogeneous Linear PDEs. 3.2. Separable Homogeneous BVP. 3.3. Equations of Mathematical Physics. 3.4. Helmholtz Equation. 3.5. Remarkable Lives and Achievements. 3.6. Exercises. 4. Symmetric Differential Operators. 4.1. Hilbert Spaces. 4.2. Orthogonal Sets of Functions. 4.3. Green Functions. 4.4. Symmetric Differential Operators. 4.5. Sturm-Liouville Differential Operators. 4.6. Remarkable Lives and Achievements. 4.7. Exercises. 5. Fourier Analysis. 5.1. Fourier Trigonometric Bases. 5.2. Fourier Series. 5.3. Convergence of Fourier Series. 5.4. Fourier Transform. 5.5. Remarkable Lives and Achievements. 5.6. Exercises. 6. Eigenfunction Expansion Method. 6.1. Preliminary Discussion: Restricted Inhomogeneities. 6.2. Application to Evolution Equations. 6.3. General Discussion: Full Inhomogeneties. 6.4. Unbounded Domains and Fourier Transform. 7. Special Functions. 7.1. Frobenius Series. 7.2. Ordinary Points. 7.3. Regular Singular Points. 7.4. Bessel Equation. 7.5. Euler Gamma Function. 7.6. Remarkable Lives and Achievements. 7.7. Exercises. 8. Cylindrical and Spherical BVPs. 8.1. Cylindrical BVPs. 8.2. Spherical BVPs. 8.3. Beyond Cylindrical and Spherical. 8.4. Exercises.
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Quantum Mechanics;Linear Partial Differential Equations;Fluid Dynamics;Mathematical Methods;Hilbert Spaces
1. Introduction. 1.1. Partial Differential Equations. 1.2. Boundary and Initial Conditions. 1.3. Local Solvability. 1.4. Characteristics. 1.5. General Solutions. 1.6. Remarkable Lives and Achievements. 2. Linear PDEs. 2.1. Linear Differential Operators. 2.2. 1D Eigenvalue Problems. 2.3. Linear BVPs in Physics. 2.4. Exercises. 3. Separation of Variables Method. 3.1. Separable Homogeneous Linear PDEs. 3.2. Separable Homogeneous BVP. 3.3. Equations of Mathematical Physics. 3.4. Helmholtz Equation. 3.5. Remarkable Lives and Achievements. 3.6. Exercises. 4. Symmetric Differential Operators. 4.1. Hilbert Spaces. 4.2. Orthogonal Sets of Functions. 4.3. Green Functions. 4.4. Symmetric Differential Operators. 4.5. Sturm-Liouville Differential Operators. 4.6. Remarkable Lives and Achievements. 4.7. Exercises. 5. Fourier Analysis. 5.1. Fourier Trigonometric Bases. 5.2. Fourier Series. 5.3. Convergence of Fourier Series. 5.4. Fourier Transform. 5.5. Remarkable Lives and Achievements. 5.6. Exercises. 6. Eigenfunction Expansion Method. 6.1. Preliminary Discussion: Restricted Inhomogeneities. 6.2. Application to Evolution Equations. 6.3. General Discussion: Full Inhomogeneties. 6.4. Unbounded Domains and Fourier Transform. 7. Special Functions. 7.1. Frobenius Series. 7.2. Ordinary Points. 7.3. Regular Singular Points. 7.4. Bessel Equation. 7.5. Euler Gamma Function. 7.6. Remarkable Lives and Achievements. 7.7. Exercises. 8. Cylindrical and Spherical BVPs. 8.1. Cylindrical BVPs. 8.2. Spherical BVPs. 8.3. Beyond Cylindrical and Spherical. 8.4. Exercises.
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