"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Formal calculus with DERIVE and MAPLE
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MT029
4
2+1+0
5
optional
Informatică
MT029
4
2+1+0
5
optional
Informatică
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