Applications of Computer Algebra (eBook, PDF)

Redaktion: Pavelle, Richard

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 448
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781468468885
• Artikelnr.: 43994490

Inhaltsangabe

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.