- Book
- x, 454 p. : ill. ; 24 cm.
- Chapter 1: Where PDEs Come From 1.1 What is a Partial Differential Equation? 1.2 First-Order Linear Equations 1.3 Flows, Vibrations, and Diffusions 1.4 Initial and Boundary Conditions 1.5 Well-Posed Problems 1.6 Types of Second-Order EquationsChapter 2: Waves and Diffusions 2.1 The Wave Equation 2.2 Causality and Energy 2.3 The Diffusion Equation 2.4 Diffusion on the Whole Line 2.5 Comparison of Waves and DiffusionsChapter 3: Reflections and Sources 3.1 Diffusion on the Half-Line 3.2 Reflections of Waves 3.3 Diffusion with a Source 3.4 Waves with a Source 3.5 Diffusion RevisitedChapter 4: Boundary Problems 4.1 Separation of Variables, The Dirichlet Condition 4.2 The Neumann Condition 4.3 The Robin ConditionChapter 5: Fourier Series 5.1 The Coefficients 5.2 Even, Odd, Periodic, and Complex Functions 5.3 Orthogonality and the General Fourier Series 5.4 Completeness 5.5 Completeness and the Gibbs Phenomenon 5.6 Inhomogeneous Boundary ConditionsChapter 6: Harmonic Functions 6.1 Laplace's Equation 6.2 Rectangles and Cubes 6.3 Poisson's Formula 6.4 Circles, Wedges, and AnnuliChapter 7: Green's Identities and Green's Functions 7.1 Green's First Identity 7.2 Green's Second Identity 7.3 Green's Functions 7.4 Half-Space and SphereChapter 8: Computation of Solutions 8.1 Opportunities and Dangers 8.2 Approximations of Diffusions 8.3 Approximations of Waves 8.4 Approximations of Laplace's Equation 8.5 Finite Element MethodChapter 9: Waves in Space 9.1 Energy and Causality 9.2 The Wave Equation in Space-Time 9.3 Rays, Singularities, and Sources 9.4 The Diffusion and Schrodinger Equations 9.5 The Hydrogen AtomChapter 10: Boundaries in the Plane and in Space 10.1 Fourier's Method, Revisited 10.2 Vibrations of a Drumhead 10.3 Solid Vibrations in a Ball 10.4 Nodes 10.5 Bessel Functions 10.6 Legendre Functions 10.7 Angular Momentum in Quantum MechanicsChapter 11: General Eigenvalue Problems 11.1 The Eigenvalues Are Minima of the Potential Energy 11.2 Computation of Eigenvalues 11.3 Completeness 11.4 Symmetric Differential Operators 11.5 Completeness and Separation of Variables 11.6 Asymptotics of the EigenvaluesChapter 12: Distributions and Transforms 12.1 Distributions 12.2 Green's Functions, Revisited 12.3 Fourier Transforms 12.4 Source Functions 12.5 Laplace Transform TechniquesChapter 13: PDE Problems for Physics 13.1 Electromagnetism 13.2 Fluids and Acoustics 13.3 Scattering 13.4 Continuous Spectrum 13.5 Equations of Elementary ParticlesChapter 14: Nonlinear PDEs 14.1 Shock Waves 14.2 Solitions 14.3 Calculus of Variations 14.4 Bifurcation Theory 14.5 Water WavesAppendix A.1 Continuous and Differentiable Functions A.2 Infinite Sets of Functions A.3 Differentiation and Integration A.4 Differential Equations A.5 The Gamma FunctionReferencesAnswers and Hints to Selected ExercisesIndex.
- (source: Nielsen Book Data)9780470054567 20160528
(source: Nielsen Book Data)9780470385531 20160527
- Chapter 1: Where PDEs Come From 1.1 What is a Partial Differential Equation? 1.2 First-Order Linear Equations 1.3 Flows, Vibrations, and Diffusions 1.4 Initial and Boundary Conditions 1.5 Well-Posed Problems 1.6 Types of Second-Order EquationsChapter 2: Waves and Diffusions 2.1 The Wave Equation 2.2 Causality and Energy 2.3 The Diffusion Equation 2.4 Diffusion on the Whole Line 2.5 Comparison of Waves and DiffusionsChapter 3: Reflections and Sources 3.1 Diffusion on the Half-Line 3.2 Reflections of Waves 3.3 Diffusion with a Source 3.4 Waves with a Source 3.5 Diffusion RevisitedChapter 4: Boundary Problems 4.1 Separation of Variables, The Dirichlet Condition 4.2 The Neumann Condition 4.3 The Robin ConditionChapter 5: Fourier Series 5.1 The Coefficients 5.2 Even, Odd, Periodic, and Complex Functions 5.3 Orthogonality and the General Fourier Series 5.4 Completeness 5.5 Completeness and the Gibbs Phenomenon 5.6 Inhomogeneous Boundary ConditionsChapter 6: Harmonic Functions 6.1 Laplace's Equation 6.2 Rectangles and Cubes 6.3 Poisson's Formula 6.4 Circles, Wedges, and AnnuliChapter 7: Green's Identities and Green's Functions 7.1 Green's First Identity 7.2 Green's Second Identity 7.3 Green's Functions 7.4 Half-Space and SphereChapter 8: Computation of Solutions 8.1 Opportunities and Dangers 8.2 Approximations of Diffusions 8.3 Approximations of Waves 8.4 Approximations of Laplace's Equation 8.5 Finite Element MethodChapter 9: Waves in Space 9.1 Energy and Causality 9.2 The Wave Equation in Space-Time 9.3 Rays, Singularities, and Sources 9.4 The Diffusion and Schrodinger Equations 9.5 The Hydrogen AtomChapter 10: Boundaries in the Plane and in Space 10.1 Fourier's Method, Revisited 10.2 Vibrations of a Drumhead 10.3 Solid Vibrations in a Ball 10.4 Nodes 10.5 Bessel Functions 10.6 Legendre Functions 10.7 Angular Momentum in Quantum MechanicsChapter 11: General Eigenvalue Problems 11.1 The Eigenvalues Are Minima of the Potential Energy 11.2 Computation of Eigenvalues 11.3 Completeness 11.4 Symmetric Differential Operators 11.5 Completeness and Separation of Variables 11.6 Asymptotics of the EigenvaluesChapter 12: Distributions and Transforms 12.1 Distributions 12.2 Green's Functions, Revisited 12.3 Fourier Transforms 12.4 Source Functions 12.5 Laplace Transform TechniquesChapter 13: PDE Problems for Physics 13.1 Electromagnetism 13.2 Fluids and Acoustics 13.3 Scattering 13.4 Continuous Spectrum 13.5 Equations of Elementary ParticlesChapter 14: Nonlinear PDEs 14.1 Shock Waves 14.2 Solitions 14.3 Calculus of Variations 14.4 Bifurcation Theory 14.5 Water WavesAppendix A.1 Continuous and Differentiable Functions A.2 Infinite Sets of Functions A.3 Differentiation and Integration A.4 Differential Equations A.5 The Gamma FunctionReferencesAnswers and Hints to Selected ExercisesIndex.
- (source: Nielsen Book Data)9780470054567 20160528
(source: Nielsen Book Data)9780470385531 20160527
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | |
QA374 .S86 2008 | Unknown On reserve at Li and Ma Science Library 2-hour loan |
QA374 .S86 2008 | Unknown On reserve at Li and Ma Science Library 2-hour loan |
QA374 .S86 2008 | Unknown On reserve at Li and Ma Science Library 2-hour loan |
MATH-220-01
- Course
- MATH-220-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Ryzhik, Leonid
- Book
- xii, 371 p. : ill. ; 26 cm.
- 1. Introduction-- 2. First-order equations-- 3. Second-order linear equations-- 4. The 1D wave equation-- 5. Separation of variables-- 6. Sturm-Liouville problem-- 7. Elliptic equations-- 8. Green's function and integral representation-- 9. Equations in high dimensions-- 10. Variational methods-- 11. Numerical methods-- 12. Solutions of odd-numbered problems.
- (source: Nielsen Book Data)9780521613231 20160604
(source: Nielsen Book Data)9780521613231 20160604
- 1. Introduction-- 2. First-order equations-- 3. Second-order linear equations-- 4. The 1D wave equation-- 5. Separation of variables-- 6. Sturm-Liouville problem-- 7. Elliptic equations-- 8. Green's function and integral representation-- 9. Equations in high dimensions-- 10. Variational methods-- 11. Numerical methods-- 12. Solutions of odd-numbered problems.
- (source: Nielsen Book Data)9780521613231 20160604
(source: Nielsen Book Data)9780521613231 20160604
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | |
QA374 .P54 2005 | Unknown On reserve at Li and Ma Science Library 2-hour loan |
QA374 .P54 2005 | Unknown On reserve at Li and Ma Science Library 2-hour loan |
MATH-220-01
- Course
- MATH-220-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Ryzhik, Leonid