Symbolic Computation
Symbolic Computation

Author: Robert Grossman

Publisher: SIAM

Published: 1989-01-01

Total Pages: 191

ISBN-13: 9781611971033

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This is a monograph that describes current research efforts in the application of symbolic computation to several areas, including dynamical systems, differential geometry, Lie algebras, numerical analysis, fluid dynamics, perturbation theory, control theory, and mechanics. The chapters, which illustrate how symbolic computations can be used to study various mathematical structures, are outgrowths of the invited talks that were presented at the NASA-Ames Workshop on The Use of Symbolic Methods to Solve Algebraic and Geometric Problems Arising in Engineering. More than 100 people participated in the two-day conference, which took place in January 1987 at the NASA-Ames Research Center in Moffett Field, California. The field of symbolic computation is becoming increasingly important in science, engineering, and mathematics. The availability of powerful computer algebra systems on workstations has made symbolic computation an important tool for many researchers.

Functional Calculus of Pseudo-Differential Boundary Problems
Functional Calculus of Pseudo-Differential Boundary Problems

Author: G. Grubb

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 520

ISBN-13: 1475718985

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CHAPTER 1. STANDARD PSEUDO-DIFFERENTIAL BOUNDARY PROBLEMS AND THEIR REALIZATIONS 1. 1 Introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 2 The calculus of pseudo-differential boundary problems . . •. 19 1. 3 Green's formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1. 4 Realizations and normal boundary conditions . . . . . . . . . . . . . . 39 1. 5 Parameter-ellipticity and parabolicity . . . . . . . . . . . . . . . . . . . 50 1. 6 Adjoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 1. 7 Semiboundedness and coerciveness . . . . . . . . •. . . . . . . . . . . •. . . . 96 CHAPTER 2. THE CALCULUS OF PARAMETER-DEPENDENT OPERATORS 2. 1 Parameter-dependent pseudo-differential operators . . •. . . . . 125 2. 2 The transmission property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 2. 3 Parameter-dependent boundary symbol s . . . . . . . . . . . . . . . . . . . . . 179 2. 4 Operators and kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 2. 5 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 2. 6 Composition of xn-independent boundary symbol operators . . 234 2. 7 Compositions in general . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 2. 8 Strictly homogeneous symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 CHAPTER 3. PARAMETRIX AND RESOLVENT CONSTRUCTIONS 3. 1 Ellipticity. Auxiliary elliptic operators . . . . . . . . . . . . . . . . 280 3. 2 The parametrix construction . . . . . . . . . . •. . . . . . . . . . . . . . . . . . . 297 3. 3 The resolvent of a realization . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 3. 4 Other special cases . . . . . . •. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 CHAPTER 4. SOME APPLICATIONS 4. 1 Evolution problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 4. 2 The heat operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4. 3 An index formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 4. 4 Complex powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 4. 5 Spectral asymptotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 4. 6 Implicit eigenvalue problems . . . . . . . . . . . . . . . . . . . . . . . •. . . . . 437 4. 7 Singular perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 APPENDIX. VARIOUS PREREQUISITES (A. 1 General notation. A. 2 Functions and distributions. A. 3 Sobolev spaces. A. 4 Spaces over sub sets of mn. A. 5 Spaces over manifolds. A. 6 Notions from 473 spectral theory. ) '" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BIBLIOGRAPHY . . . •. . . . . . . •. . . . . . . . . . . . . . . •. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Symbolic Computation
Symbolic Computation

Author: Edward L. Green

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 252

ISBN-13: 9780821856222

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This volume presents the proceedings from the research conference, ''Symbolic Computation: Solving Equations in Algebra, Analysis, and Engineering,'' held at Mount Holyoke College (MA). It provides an overview of current research in symbolic computation as it applies to the solution of polynomial systems. The conference brought together pure and applied mathematicians, computer scientists, and engineers, who use symbolic computation to solve systems of equations or who develop thetheoretical background and tools needed for this purpose. Within this general framework, the conference focused on several themes: systems of polynomials, systems of differential equations, noncommutative systems, and applications.