1  5
Number of results to display per page
 Vasy, András, author.
 Providence, Rhode Island : American Mathematical Society, [2015]
 Description
 Book — x, 281 pages : illustrations ; 27 cm.
 Summary

 * 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)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA377 .V38 2015  Unknown On reserve at Li and Ma Science Library 1day loan 
MATH17301
 Course
 MATH17301  Theory of Partial Differential Equations
 Instructor(s)
 Fredrickson, Laura Joy
2. Partial differential equations [2010]
 Evans, Lawrence C., 1949
 2nd ed.  Providence, R.I. : American Mathematical Society, 2010.
 Description
 Book — 749 p. ; 26 cm.
 Summary

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)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA377 .E95 2010  Unknown On reserve at Li and Ma Science Library 1day loan 
MATH17301
 Course
 MATH17301  Theory of Partial Differential Equations
 Instructor(s)
 Fredrickson, Laura Joy
 Strauss, Walter A., 1937
 2nd ed.  Hoboken, N.J. ; Chichester : Wiley, 2008.
 Description
 Book — x, 454 p. : ill. ; 24 cm.
 Summary

 Chapter 1: Where PDEs Come From 1.1 What is a Partial Differential Equation? 1.2 FirstOrder Linear Equations 1.3 Flows, Vibrations, and Diffusions 1.4 Initial and Boundary Conditions 1.5 WellPosed Problems 1.6 Types of SecondOrder Equations
 Chapter 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 Diffusions
 Chapter 3: Reflections and Sources 3.1 Diffusion on the HalfLine 3.2 Reflections of Waves 3.3 Diffusion with a Source 3.4 Waves with a Source 3.5 Diffusion Revisited
 Chapter 4: Boundary Problems 4.1 Separation of Variables, The Dirichlet Condition 4.2 The Neumann Condition 4.3 The Robin Condition
 Chapter 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 Conditions
 Chapter 6: Harmonic Functions 6.1 Laplace's Equation 6.2 Rectangles and Cubes 6.3 Poisson's Formula 6.4 Circles, Wedges, and Annuli
 Chapter 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 HalfSpace and Sphere
 Chapter 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 Method
 Chapter 9: Waves in Space 9.1 Energy and Causality 9.2 The Wave Equation in SpaceTime 9.3 Rays, Singularities, and Sources 9.4 The Diffusion and Schrodinger Equations 9.5 The Hydrogen Atom
 Chapter 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 Mechanics
 Chapter 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 Eigenvalues
 Chapter 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 Techniques
 Chapter 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 Particles
 Chapter 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)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA374 .S86 2008  Unknown On reserve at Li and Ma Science Library 1day loan 
QA374 .S86 2008  Unknown On reserve at Li and Ma Science Library 1day loan 
QA374 .S86 2008  Unknown On reserve at Li and Ma Science Library 1day loan 
MATH17301
 Course
 MATH17301  Theory of Partial Differential Equations
 Instructor(s)
 Fredrickson, Laura Joy
 Pinchover, Yehuda, 1953
 New York : Cambridge University Press, 2005.
 Description
 Book — xii, 371 p. : ill. ; 26 cm.
 Summary

 1. Introduction
 2. Firstorder equations
 3. Secondorder linear equations
 4. The 1D wave equation
 5. Separation of variables
 6. SturmLiouville 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 oddnumbered problems.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA374 .P54 2005  Unknown On reserve at Li and Ma Science Library 1day loan 
QA374 .P54 2005  Unknown On reserve at Li and Ma Science Library 1day loan 
MATH17301
 Course
 MATH17301  Theory of Partial Differential Equations
 Instructor(s)
 Fredrickson, Laura Joy
5. Partial differential equations [1998]
 Evans, Lawrence C., 1949
 Providence, R.I. : American Mathematical Society, c1998.
 Description
 Book — xvii, 662 p. : ill. ; 26 cm.
 Summary

 Introduction Part I: Representation formulas for solutions: Four important linear partial differential equations Nonlinear firstorder PDE Other ways to represent solutions Part II: Theory for linear partial differential equations: Sobolev spaces Secondorder elliptic equations Linear evolution equations Part III: Theory for nonlinear partial differential equations: The calculus of variations Nonvariational techniques HamiltonJacobi equations Systems of conservation laws Appendices Bibliography Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Green Library, Science Library (Li and Ma)
MATH17301
 Course
 MATH17301  Theory of Partial Differential Equations
 Instructor(s)
 Fredrickson, Laura Joy