list1 = {a, b, c, d}

list2 = Table[i, {i, 1, 4}]

pairs = Thread[{list1, list2}]

scalprod = Dot[list1, list2]

(matrix = 
          Table[Table["a" <> ToString[i] <> ToString[j], {i, 1, 4}], {j, 
              1, 5}]) // MatrixForm

fun[x_, y_] = x^2 + y^2;
Plot[fun[x, 0], {x, -1, 1}]

ContourPlot[fun[x, y], {x, -1, 1}, {y, -1, 1}]

n = 10;
xvec = Table[-1 +  i/10, {i, 0, 20}]
yvec = Sin[Pi xvec];
xy = Thread[{xvec, yvec}];
ListPlot[xy, PlotStyle -> PointSize[0.02]]

Heaviside[x_ /; x > 0] := 1;
Heaviside[x_ /; x <= 0] := 0;
Plot[Heaviside[x], {x, -1, 1}]

(* 
      Introduce Ledge function for displaying the piecewise solution *) 
Ledge[c_, x_, d_] = 
        UnitStep[x - c + d] - 
          UnitStep[x - c - d];
Plot[Ledge[0, x, a], {x, -0.1, 0.1}]