Faculty of Mathematics and Computer Science

Formal calculus with DERIVE and MAPLE |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

Teaching Staff in Charge |

Assoc.Prof. ANISIU Valer, Ph.D., anisiu@math.ubbcluj.ro |

Aims |

A general presentation of CAS (Computer Algebra Systems) with special
attention on DERIVE 5 and MAPLE. The emphasis is on the types of mathematical problems which can be handled with such symbolic tools; several algorithms are considered in order to extend the capabilities of these systems. |

Content |

1. The syntax in DERIVE 5 and MAPLE: expressions and their types, iterates,
functions. Evaluation rules. 2. Programming in DERIVE 5 and MAPLE (functions and procedures, local and global variables, configuration for the mathematical environment, existent packages) 3. Applications to: - Number theory and combinatorics (prime numbers, "probalistic" algorithms) - Matrix calculus and linear algebra (bases, kernels, ranges, orthogonalizations, Gauss-Jordan forms, eigenvectors, Jordan forms) - Polynomials of one and several variables (computations in Zn[X}, Grobner basis) - Recurrent sequences (linear and nonlinear recurrent equations) - Asymptotic expansions (asymptotic equivalents, computational methods, integrals depending on parameters) - Differential and integral calculus (simple and multiple integrals, integration on manifolds) - Topology (topologies on finite sets, generations of fopologies, computation for the closure operator) - Complex variable functions (analytic extensions, residues, computing integrals using the residues's theorem, conformal representations) - Graphic representation in 2D, 3D (orthogonal, polar cylindrical and spherical representations, generating tubular surfaces, rotations, animations) |

References |

1. V. Anisiu: Calcul formal cu DERIVE. Ed. MicroInformatica, Cluj 2001.
2. C. Gomez, B. Salvy, P. Zimmermann: Calcul Formel: mode d'emploi, exemples en MAPLE. Masson, Paris 1995 3. Andre Heck: Introduction to Maple, 2nd edition, Springer 1996 4. E. Scheiber, M. Lupu: Matematici speciale; Rezolvarea problemelor asistata de calculator cu exemplificari in Derive, Mathcad, Maple, Mathematica. Ed. Stiintifica, Bucuresti 1998. 5. G. Korn, T. Korn: Mathematical Handbook for Scientists and Engineers, McGrawiHill 1968 6. M. Chossat: Mathematiques de l'ingenieur. Dunod, Paris, 1996 |

Assessment |

Projects and exam |