Today, certain computer software systems exist which surpass the computational ability of researchers when their mathematical techniques are applied to many areas of science and engineering. These computer systems can perform a large portion of the calculations seen in mathematical analysis. Despite this massive power, thousands of people use these systems as a routine resource for everyday calculations. These software programs are commonly called "Computer Algebra" systems. They have names such as MACSYMA, MAPLE, muMATH, REDUCE and SMP. They are receiving credit as a computational aid with in creasing regularity in articles in the scientific and engineering literature. When most people think about computers and scientific research these days, they imagine a machine grinding away, processing numbers arithmetically. It is not generally realized that, for a number of years, computers have been performing non-numeric computations. This means, for example, that one inputs an equa tion and obtains a closed form analytic answer. It is these Computer Algebra systems, their capabilities, and applications which are the subject of the papers in this volume.
Author(s): Richard Pavelle (auth.), Richard Pavelle (eds.)
Edition: 1
Publisher: Springer US
Year: 1985
Language: English
Pages: 448
Tags: Mathematical Software; Symbolic and Algebraic Manipulation; Algebra
Front Matter....Pages i-x
MACSYMA: Capabilities and Applications to Problems in Engineering and the Sciences....Pages 1-61
Modern Symbolic Mathematical Computation Systems....Pages 62-73
Using VAXIMA to Write FORTRAN Code....Pages 74-94
Applications of Symbolic Mathematics to Mathematics....Pages 95-111
Past, Present, and Future Applications of Computer Algebra in Chemistry....Pages 112-118
Symbolic Computation in Chemical Education....Pages 119-146
A LISP System for Chemical Groups: Wigner — Eckart Coefficients for Arbitrary Permutation Groups....Pages 147-168
Polymer Modeling Applications of Symbolic Computation....Pages 169-182
Stability Analysis and Optimal Control of a Photochemical Heat Engine....Pages 183-209
Fourier Transform Algorithms for Spectral Analysis Derived with MACSYMA....Pages 210-240
Computer Algebra as a Tool for Solving Optimal Control Problems....Pages 241-261
Application of MACSYMA to Kinematics and Mechanical Systems....Pages 262-280
Stability Analysis of a Robotic Mechanism Using Computer Albegra....Pages 281-292
Derivation of the Hopf Bifurcation Formula Using Lindstedt’s Perturbation Method and MACSYMA....Pages 293-308
Normal Form and Center Manifold Calculations on MACSYMA....Pages 309-328
Symbolic Computation of the Stokes Wave....Pages 329-337
Simplifying Large Algebraic Expressions by Computer....Pages 338-391
A Proposal for the Solution of Quantum Field Theory Problems Using a Finite-Element Approximation....Pages 392-406
Exact Solutions for Superlattices and How to Recognize them with Computer Algebra....Pages 407-414
Computer Generation of Symbolic Generalized Inverses and Applications to Physics and Data Analysis....Pages 415-426
Back Matter....Pages 427-433
