Komech, A. & Komech, A.
Principles of Partial Differential Equations
Springer-Verlag 2009.10
161 pp.(H)
ISBN 1-4419-1095-6
7,600円
Contents
1. Hyperbolic equations.Method of characteristics/ 2. The Fourier method/ 3. Distributions and Green’s functions/ 4. Fundamental solutions and Green’s functions in higher dimensions/ References/ Index/
* This concise book covers the classical tools of PDE theory used in today's science and engineering: characteristics, the wave propagation, the Fourier method, distributions, Sobolev spaces, fundamental solutions, and Green's functions. The approach is problem-oriented, giving the reader an opportunity to master solution techniques. *
Bove, A. et al. ed.
Advances in Phase Space Analysis of Partial Differential Equations
In Honor of Ferruccio Colombini's 60th Birthday
Birkhauser 2009.10
302 pp.(H)
ISBN 0-8176-4860-7
17,700円
Contents
1.Tangent Halfspaces to Sets of Finite Perimeter in Carnot Groups/ 2.The Heat Kernel and Frequency Localized Functions on the Heisenberg Group Hajer Bahouri and Isabelle Gallagher/ 3.Shiferaw Berhanu and Jorge Hounie/ 4.Operators/ 5.The Solvability and Subellipticity of Systems of Pseudodifferential Operators/ 6.Uniform Exponential Decay for Viscous Damped Systems/ 7.The Hyperbolic Symmetrizer: Theory and Applications/ 8.Time Global Solutions to the Cauchy Problem for Multidimensional Kirchhoff Equations/ 9.The Order of Accuracy of Quadrature Formulae for Periodic Functions/ 10.A Note on the Oseen Kernels/ 11.Instability Behavior and Loss of Regularity/ 12.Decay Estimates for Variable Coefficient Wave Equations in Exterior Domains/ 13.On Gevrey Well-Posedness of the Cauchy Problem for Some Noneffectively Hyperbolic Operators/ 14.Singularities of the Scattering Kernel Related to Trapping Rays/ 15.Analytic Hypoellipticity for a Sum of Squares of Vector Fields in R3 Whose Poisson Stratification Consists of a Single Symplectic Stratum of Codimension Four/ 16.Multidimensional Soliton Integrodifferential Systems/ 17.Selected Lectures in Microlocal Analysis/ Index/
* This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations. *
Sachdev, P. L. & Rao, Ch. Srinivasa
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Springer-Verlag 2009.10
231 pp.(H)
ISBN 0-387-87808-4
15,400円
Contents
1. Introduction/ 2. Large Time Asymptotics for Solutions of Nonlinear First-Order Partial Differential Equations/ 3. Large Time Asymptotic Analysis of Some Nonlinear Parabolic Equations - Some Constructive Approaches/ 4. Self-similar Solutions as Large Time Asymptotics for Some Nonlinear Parabolic Equations/ 5. Asymptotics in Fluid Mechanics/ Index/
* A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations. These approaches, in conjunction with modern computational methods, help solve physical problems in a satisfactory manner. *
Atkinson, K.E. et al.
Numerical Solution of Ordinary Differential Equations
(Pure and Applied Mathematics)
John Wiley & Sons 2009.2
252 pp.(H)
ISBN 0-470-04294-X
10,700円
Contents
1. Theory of differential equations: an introduction/ 2. Euler's method/ 3. Systems of differential equations/ 4. The backward Euler method and the trapezoidal method/ 5. Taylor and Runge-Kutta methods/ 6. Multistep methods/ 7. General error analysis for multistep methods/ 8. Stiff differential equations/ 9. Implicit RK methods for stiff differential equations/ 10. Differential algebraic equations/ 11. Two-point boundary value problems/ 12. Volterra integral equations/ Appendix A: Taylor's theorem/ Appendix B: Polynomial interpolation/ Bibliography/ Index/ *
Abell, M. & Braselton, J.
Introductiory Differential Equations 3rd ed.
with Boundary Value Problems
Academic Press 2009.10
744 pp.(H)
ISBN 0-12-374935-2
16,800円
Contents
1.Introduction to Differential Equations/ 2.First-Order Equations/ 3.Applications of First-Order Equations/ 4.Higher Order Equations/ 5.Applications of Higher Order Equations/ 6.Systems of Differential Equationsl/ 7.Applications of First-Order Systems/ 8.Laplace Transforms/ 9.Eigenvalue Problems and Fourier Series/ 10.Partial Differential Equations/ 11.Answers, Hints and Solutions to Selected Exercises/ Index/
* This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, Fourier Series and Boundary Value Problems. The text is appropriate for two semester courses: the first typically emphasizes ordinary differential equations and their applications while the second emphasizes special techniques (like Laplace transforms) and partial differential equations. The texts follows a "traditional" curriculum and takes the "traditional" (rather than "dynamical systems") approach. *
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