By John L. Morris

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**Additional info for Conference on Applications of Numerical Analysis**

**Example text**

In this upgrade, Mathematica has been substantially redesigned in its internal architecture for better functionality. It increases interactivity, more adaptive visualization, ease of data integration, symbolic interface construction among others new features. 2 Basic Features Symbolic, numerical, acoustic, and graphical computations; Extensibility, elegance; Available for MS Windows, Linux, UNIX, Mac OS operating systems; Powerful and logical language; Extensive library of mathematical functions and specialized packages; An interactive front end with notebook interface; Interactive mathematical typesetting system.

F[x_,y_]:=1-Sin[x^2+y^2]; {N[f[1,2]], f[0,a], Simplify[f[a,b]]} f1=Function[{x,y},1-Sin[x^2+y^2]]; {N[f1[1,2]], f1[0,a], Simplify[f1[a,b]]} Problem: Deﬁne the vector function h(x, y) = cos(x − y), sin(x − y) and calculate h(1, 2), h(π, −π), and h cos(a2 ), cos(1 − a2 ) . 3 Mathematica Language 35 Problem: For the functions f (x) = x2 and h(x) = x + sin x calculate the composition functions (f ◦ h ◦ f )(x) and (f ◦ f ◦ f ◦ f )(x). f[x_]:=x^2; fF:=#1^2&; hF:=#1+Sin[#1]&; {fF@hF@fF[x],fF@fF@fF@fF[x],Nest[f,x,4],NestList[f,x,4]} Piecewise continuous functions can be deﬁned using the conditional operator /; or the functions Piecewise and UnitStep.

3). m)]; Matrix1:=matrix(2,2,(i,j)->i+j); Vector1:=vector(2,i->i^2); with(LinearAlgebra):ZeroMatrix(3,3);IdentityMatrix(3,3); Operations with sets, matrices: the union and intersection of sets, removing elements from sets, the sum, diﬀerence, multiplication, division, scalar multiplication of matrices, union, intersect, minus, remove,has, evalm, &*. Set3 := Set1 union Set2; Set3 := Set1 intersect Set2; Set3 := Set1 minus Set2; Set2 := remove(has, Set1, A1); Mat3 := evalm(M1 &* M2); Apply a function to each element of a structure, map.