Ambrosio, L. et al.
Calculus of Variations and Non-Linear Partial Differential Equations
Springer-Verlag 2008.
204 pp.(P)
ISBN 3-540-75913-1
7,500円
Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27 - July 2, 2005 With a historical overview by Elvira Mascolo
Contents
Part.1:Transport Equation and Cauchy Problem for Non-Smooth Vector Fields: 1. Introduction/ 2. Transport Equation and Continuity Equation within the Cauchy-Lipschitz Framework/ 3. ODE Uniqueness versus PDE Uniqueness/ 4. Vector Fields with a Sobolev Spatial Regularity/ 5. Vector Fields with a BV Spatial Regularity/ 6. Applications/ 7. Open Problems, Bibliographical Notes, and References/ Part.2:Issues in Homogenization for Problems with Non Divergence Structure: 1. Introduction/ 2. Homogenization of a Free Boundary Problem: Capillary Drops/ 3. The Construction of Plane Like Solutions to Periodic Minimal Surface Equations/ 4. Existence of Homogenization Limits for Fully Nonlinear Equations/ Part.3:A Visit with the ∞-Laplace Equation: 1. Notation/ 2. The Lipschitz Extension/Variational Problem/ 3. From∞-Subharmonic to ∞-Superharmonic/ 4. More Calculus of ∞-Subharmonic Functions/ 5. Existence and Uniqueness/ 6. The Gradient Flow and the Variational Problem for |Du| L∞/ 7. Linear on All Scales/ 8. An Impressionistic History Lesson/ 9. Generalizations, Variations, Recent Developments and Games/ Part.4:Weak KAM Theory and Partial Differential Equations: 1. Overview, KAM theory/ 2. Weak KAM Theory: Lagrangian Methods/ 3. Weak KAM Theory: Hamiltonian and PDE Methods/ 4. An Alternative Variational/PDE Construction/ 5. Some Other Viewpoints and Open Questions/ Part.5:Geometrical Aspects of Symmetrization: 1. Sets of finite perimeter/ 2. Steiner Symmetrization of Sets of Finite Perimeter/ 3. The Polya - Szego Inequality/ Index/ *
Schwarz, F.
Algorithmic Lie Theory for Solving Ordinary Differential Equations
Chapman & Hall 2007.10
448 pp.(H)
ISBN 1-5848-8889-X
11,200円
Contents
1.Introduction/ 2.Linear Differential Equations/ 3.Lie Transformation Groups/4. Equivalence and Invariants of Differential Equations/ 5.Symmetries of Differential Equations/6.Transformation to Canonical Form/ 7.Solution Algorithms. Concluding Remarks/ 8. Appendices/ 9.References/ Index/
* Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete problems. Taking this approach, Algorithmic Lie Theory for Solving Ordinary Differential Equations serves as a valuable introduction for solving differential equations using Lie's theory and related results. *
Strauss, W. A.
Partial Differential Equations 2nd ed.
偏微分方程式 第2版
John Wiley & Sons 2007.12
454 pp.(H)
ISBN 0-470-05456-5
15,100円
Contents
* Covers the fundamental properties of partial differential equations (PDEs) and proven techniques useful in analyzing them. Uses a broad approach to illustrate the rich diversity of phenomena such as vibrations of solids, fluid flow, molecular structure, photon and electron interactions, radiation of electromagnetic waves encompassed by this subject as well as the role PDEs play in modern mathematics, especially geometry and analysis. *
Cojocarn, A. & Murty, M.R.
An Introduction to Sieve Methods and Their Applications
ふるい法とその応用
Cambridge University Press 2006.1
236 pp.(H)
ISBN 0-521-84816-4
14,400円
Contents
1. Some basic notions; 2. Some elementary sieves; 3. The normal order method; 4. The Turan sieve; 5. The sieve of Eratosthenes; 6. Brun's sieve; 7. Selberg's sieve; 8. The large sieve; 9. The Bombieri-Vinogradov theorem; 10. The lower bound sieve; 11. New directions in sieve theory; Bibliography./
* Sieve theory has a rich and romantic history. The ancient question of whether there exist infinitely many twin primes (primes p such that p+2 is also prime), and Goldbach's conjecture that every even number can be written as the sum of two prime numbers, have been two of the problems that have inspired the development of the theory. This book provides a motivating introduction to sieve theory. Rather than focus on technical details which can obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. The text can be used for a senior level undergraduate course or an introductory graduate course in analytic number theory. *
Salsa,S.
Partial Differential Equations in Action
From Modelling to Theory
Springer-Verlag 2008.
450 pp.(P)
ISBN 88-470-0751-8
7,600円
Contents
* The main purpose is on the one hand to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences; on the other hand to give them a solid theoretical background for numerical methods, such as finite elements.
* Accordingly, this textbook is divided into two parts. The first one has a rather elementary character with the goal of developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. Ideas and connections with concrete aspects are emphasized whenever possible, in order to provide intuition and feeling for the subject. For this part, a knowledge of advanced calculus and ordinary differential equations is required. Also, the repeated use of the method of separation of variables assumes some basic results from the theory of Fourier series, which are summarized in an appendix. The main topic of the second part is the development of Hilbert space methods for the variational formulation and analysis of linear boundary and initial-boundary value problems\emph{. }% Given the abstract nature of these chapters, an effort has been made to provide intuition and motivation for the various concepts and results. *
Smith, R. T. & Minton, R. B. ed.
Calculus, Multivariable 3rd ed.
Late Transcendental Functions
McGraw-Hill 2007.1
1253(H)
ISBN 0-07-331420-X
16,500円
Contents
0. Preliminaries/ 1. Limits and Continuity/ 2. Differentiation/ 3. Applications of Differentiation/ 4. Integration/ 5. Applications of the Definite Integral/ 6. Exponentials, Logarithms and other Transcendental Functions/ 7. First-Order Differential Equations/ 8. First-Order Differential Equations/ 9. Infinite Series/ 10. Parametric Equations and Polar Coordinates/ 11. Vectors and the Geometry of Space/ 12. Vector-Valued Functions/ 13. Functions of Several Variables and Partial Differentiation/ 14. Multiple Integrals/ 15. Vector Calculus/ 16. Second-Order Differential Equations/ Appendix A: Proofs of Selected Theorems/ Appendix B: Answers to Odd-Numbered Exercises/ Index/
* Smith/Minton: Mathematically Precise. Student-Friendly. Superior Technology. Students who have used Smith/Minton's Calculus say it was easier to read than any other math book they've used. That testimony underscores the success of the authors’ approach which combines the most reliable aspects of mainstream Calculus teaching with the best elements of reform, resulting in a motivating, challenging book. Smith/Minton wrote the book for the students who will use it, in a language that they understand, and with the expectation that their backgrounds may have some gaps. Smith/Minton provide exceptional, reality-based applications that appeal to students’ interests and demonstrate the elegance of math in the world around us. New features include: Many new exercises and examples (for a total of 7,000 exercises and 1000 examples throughout the book) provide a careful balance of routine, intermediate and challenging exercises New exploratory exercises in every section that challenge students to make connections to previous introduced material. *
720-36 登録日 08.04.01
