- Book
- x, 281 pages : illustrations ; 27 cm.
- * Introduction* Where do PDE come from* First order scalar semilinear equations* First order scalar quasilinear equations* Distributions and weak derivatives* Second order constant coefficient PDE: Types and d'Alembert's solution of the wave equation* Properties of solutions of second order PDE: Propagation, energy estimates and the maximum principle* The Fourier transform: Basic properties, the inversion formula and the heat equation* The Fourier transform: Tempered distributions, the wave equation and Laplace's equation* PDE and boundaries* Duhamel's principle* Separation of variables* Inner product spaces, symmetric operators, orthogonality* Convergence of the Fourier series and the Poisson formula on disks* Bessel functions* The method of stationary phase* Solvability via duality* Variational problems* Bibliography* Index.
- (source: Nielsen Book Data)9781470418816 20160619
(source: Nielsen Book Data)9781470418816 20160619
- * Introduction* Where do PDE come from* First order scalar semilinear equations* First order scalar quasilinear equations* Distributions and weak derivatives* Second order constant coefficient PDE: Types and d'Alembert's solution of the wave equation* Properties of solutions of second order PDE: Propagation, energy estimates and the maximum principle* The Fourier transform: Basic properties, the inversion formula and the heat equation* The Fourier transform: Tempered distributions, the wave equation and Laplace's equation* PDE and boundaries* Duhamel's principle* Separation of variables* Inner product spaces, symmetric operators, orthogonality* Convergence of the Fourier series and the Poisson formula on disks* Bessel functions* The method of stationary phase* Solvability via duality* Variational problems* Bibliography* Index.
- (source: Nielsen Book Data)9781470418816 20160619
(source: Nielsen Book Data)9781470418816 20160619
Engineering Library (Terman)
Engineering Library (Terman) | Status |
---|---|
On reserve: Ask at circulation desk | |
QA377 .V38 2015 | Unknown 1-day loan |
CME-303-01, MATH-220-01
- Course
- CME-303-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras
- Course
- MATH-220-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras
2. Partial differential equations [2010]
- Book
- 749 p. ; 26 cm.
This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, a significantly expanded bibliography. About the First Edition: I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail...Evans' book is evidence of his mastering of the field and the clarity of presentation (Luis Caffarelli, University of Texas); It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations ...Every graduate student in analysis should read it. (David Jerison, MIT); I use Partial Differential Equations to prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's ...I am very happy with the preparation it provides my students. (Carlos Kenig, University of Chicago); Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge ...An outstanding reference for many aspects of the field. (Rafe Mazzeo, Stanford University. (GSM/19.R).
(source: Nielsen Book Data)9780821849743 20160603
(source: Nielsen Book Data)9780821849743 20160603
This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, a significantly expanded bibliography. About the First Edition: I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail...Evans' book is evidence of his mastering of the field and the clarity of presentation (Luis Caffarelli, University of Texas); It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations ...Every graduate student in analysis should read it. (David Jerison, MIT); I use Partial Differential Equations to prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's ...I am very happy with the preparation it provides my students. (Carlos Kenig, University of Chicago); Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge ...An outstanding reference for many aspects of the field. (Rafe Mazzeo, Stanford University. (GSM/19.R).
(source: Nielsen Book Data)9780821849743 20160603
(source: Nielsen Book Data)9780821849743 20160603
Engineering Library (Terman)
Engineering Library (Terman) | Status |
---|---|
On reserve: Ask at circulation desk | |
QA377 .E95 2010 | Unknown 1-day loan |
CME-303-01, MATH-220-01
- Course
- CME-303-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras
- Course
- MATH-220-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras
- 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
Engineering Library (Terman)
Engineering Library (Terman) | Status |
---|---|
On reserve: Ask at circulation desk | |
QA374 .S86 2008 | Unknown 1-day loan |
QA374 .S86 2008 | Unknown 1-day loan |
QA374 .S86 2008 | Unknown 1-day loan |
CME-303-01, MATH-220-01
- Course
- CME-303-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras
- Course
- MATH-220-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras
- 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
Engineering Library (Terman)
Engineering Library (Terman) | Status |
---|---|
On reserve: Ask at circulation desk | |
QA374 .P54 2005 | Unknown 1-day loan |
QA374 .P54 2005 | Unknown 1-day loan |
CME-303-01, MATH-220-01
- Course
- CME-303-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras
- Course
- MATH-220-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras
5. Partial differential equations [1998]
- Book
- xvii, 662 p. : ill. ; 26 cm.
- Introduction Part I: Representation formulas for solutions: Four important linear partial differential equations Nonlinear first-order PDE Other ways to represent solutions Part II: Theory for linear partial differential equations: Sobolev spaces Second-order elliptic equations Linear evolution equations Part III: Theory for nonlinear partial differential equations: The calculus of variations Nonvariational techniques Hamilton-Jacobi equations Systems of conservation laws Appendices Bibliography Index.
- (source: Nielsen Book Data)9780821807729 20160528
(source: Nielsen Book Data)9780821807729 20160528
- Introduction Part I: Representation formulas for solutions: Four important linear partial differential equations Nonlinear first-order PDE Other ways to represent solutions Part II: Theory for linear partial differential equations: Sobolev spaces Second-order elliptic equations Linear evolution equations Part III: Theory for nonlinear partial differential equations: The calculus of variations Nonvariational techniques Hamilton-Jacobi equations Systems of conservation laws Appendices Bibliography Index.
- (source: Nielsen Book Data)9780821807729 20160528
(source: Nielsen Book Data)9780821807729 20160528
Engineering Library (Terman)
Engineering Library (Terman) | Status |
---|---|
On reserve: Ask at circulation desk | |
QA377 .E95 1998 | Unknown 1-day loan |
QA377 .E95 1998 | Unknown 1-day loan |
CME-303-01, MATH-220-01
- Course
- CME-303-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras
- Course
- MATH-220-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras
6. Partial differential equations [1981]
- Book
- x, 249 p. : ill. ; 25 cm.
Identifies significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. This book contains a chapter on Lewy's example of a linear equation without solutions.
(source: Nielsen Book Data)9780387906096 20160528
(source: Nielsen Book Data)9780387906096 20160528
Identifies significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. This book contains a chapter on Lewy's example of a linear equation without solutions.
(source: Nielsen Book Data)9780387906096 20160528
(source: Nielsen Book Data)9780387906096 20160528
Engineering Library (Terman)
Engineering Library (Terman) | Status |
---|---|
On reserve: Ask at circulation desk | |
QA374 .J6 1981 | Unknown 1-day loan |
QA374 .J6 1981 | Unknown 1-day loan |
CME-303-01, MATH-220-01
- Course
- CME-303-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras
- Course
- MATH-220-01 -- Partial Differential Equations of Applied Mathematics
- Instructor(s)
- Vasy, Andras