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.
Inhaltsverzeichnis
1. MACSYMA: Capabilities and Applications to Problems in Engineering and the Sciences. - 2. Modern Symbolic Mathematical Computation Systems. - 3. Using VAXIMA to Write FORTRAN Code. - 4. Applications of Symbolic Mathematics to Mathematics. - 5. Past, Present, and Future Applications of Computer Algebra in Chemistry. - 6. Symbolic Computation in Chemical Education. - 7. A Lisp System for Chemical Groups: Wigner Eckart Coefficients for Arbitrary Permutation Groups. - 8. Polymer Modeling Applications of Symbolic Computation. - 9. Stability Analysis and Optimal Control of a Photochemical Heat Engine. - 10. Fourier Transform Algorithms for Spectral Analysis Derived with MACSYMA. - 11. Computer Algebra as a Tool for Solving Optimal Control Problems. - 12. Application of MACSYMA to Kinematics and Mechanical Systems. - 13. Stability Analysis of a Robotic Mechanism Using Computer Algebra. - 14. Derivation of the Hopf Bifurcation Formula Using Lindstedt s Perturbation Method and MACSYMA. - 15. Normal Form and Center Manifold Calculations on MACSYMA. - 16. Symbolic Computation of the Stokes Wave. - 17. Simplifying Large Algebraic Expressions by Computer. - 18. A Proposal for the Solution of Quantum Field Theory Problems Using a Finite-Element Approximation. - 19. Exact Solutions for Superlattices and How to Recognize Them with Computer Algebra. - 20. Computer Generation of Symbolic Generalized Inverses and Applications to Physics and Data Analysis.
