Short description of computer algebra systems (CAS). History of CAS. Special purpose systems and general purpose systems.
CAS systems REDUCE, MACSYMA, DERIVE, MATCAD, Maple, Mathematica, AXIOM, etc and their history. Main properties of CAS. Advantages and limitations of CAS in scientific computing.
General principles of CAS design and development, their implementation on different platforms, using computer graphics and scientific vizualisation. Design of Maple (user interface - Iris, basic algebraic engine- kernel, external and share library, programming language).
Maple categories of basic CAS objects. Maple names and statements, composite data types, assume facility, simplification.
Programming in Maple (structure of programming language, protected names, global and system variables, a single algebraic expression, an array of algebraic expressions, operators for forming expressions, sets, sequence, lists, arrays, tables, functions and procedures, libraries of functions).
Basic inner representation of function and main principles of manipulations with expressions. Polynomials and rational functions and manipulations with their expressions. Mathematical functions. Differentiation, integration, summation, limits and series. Solving equations, solving ODE and PDE.
Using CAS for education and research. Scientific computing and mathematical modelling (problem setting and formulation of its mathematical model, scientific evaluation and its visualisation, analysis of result interpretations and a verification of solution).
Practical examples of using Maple.
GANDER, W. and Jiří HŘEBÍČEK. Solving Prolems in Scientific Computing Using Maple and MATLAB. (Solving Prolems in Scientific Computing Using Maple and MATLAB.). 3. vyd. Heidelberg: Springer Verlag, 1997. 408 pp. ISBN 3-540-61793-0. info
HECK, André. Introduction to maple. 2nd ed. New York: Springer-Verlag, 1996. xvii, 699. ISBN 0-387-94535-0. info
Assessment methods (in Czech)
během semestru jsou vyžadovány domácí práce
na závěr projekt