MATHPROGWEB.TEX ME 353 M.M. Yovanovich COMPUTER ALGEBRA SYSTEMS Computer Algebra Systems or Symb olic Mathematics Software Packages have b een de- velop ed over the past 25 years. The b est known packages are MACSYMA, MAPLE, MATHEMATICA, MATHCAD, MATHSCRIBE, MuMATH, and DERIVE, RE- DUCE, SMP. These packages will b e denoted by MATHPROG in this brief overview. MATHPROG tie together many disparate mathematical capabilities in one package. MATHPROG is at once a computer algebra system, a collection of numerical routines, and a mathematical graphics package. All the mathematics are accessed by a single command language and programming language, and the entire user interaction takes place in a uniform graphical environment. MATHPROG can b e used to do analytical work, to manipulate algebraic expressions, to di erentiate and integrate, solve linear and nonlinear ordinary di erential equations ana- lytically or numerically, display results graphically, and much more. For example MATH- PROG suchasMACSYMA, MAPLE, MATHEMATICA, MATHCAD, MATLAB as well as Spread Sheets suchas EXCEL supp ort sp ecial functions such as Airy, Bessel, er- ror, complementary error, b eta and gamma, Legendre, complete and incomplete elliptic integrals, and others. These are very imp ortant when dealing with solutions to ordinary and partial di erential equations. MATHPROG can b e used to write pro cedural programs suchas BASIC, FORTRAN, PASCAL, etc to p erform sp eci c tasks. When used prop erly MATHPROG can b e a powerful to ol to increase ones pro ductivity and to enable one to address new problems. MAPLE V release 4 is a recently develop ed system written in C in order to achieve greater p ortablilty and sp eed. MAPLE runs on a large range of machines. It is avail- able from Waterlo o Maple Software, 450 Philip Street, Waterlo o, Ontario, N2L 5JL, email: [email protected]. MAPLE V release 4 is available through WATSTAR..