Sample Calculus function definitions in Mathematica

Introduction

Functions

Environments:-

Matlab

Mathematica

Function definitions in Mathematica See also: MathTools

sample[a_,b_,n_] := N[Range[a,b,(b-a)/n]] /. 0->0.0

d[x_List] := Drop[x,1] - Drop[x,-1]

mids[x_List] := (Drop[x,1] + Drop[x,-1]) / 2

sum[x_List] := Apply[Plus,x]

S[x_List]:=FoldList[Plus, 0.0, x ]

plot[x_List, y_List] := ListPlot[Transpose[{x,y}], PlotJoined ->True]

A typical sequence to demonstrate that the derivative of the integral returns the original function might consist of

              x = sample[0,3,100];
               y = Exp[-x^2];
              Iy = S[mids[y]*d[x]];
            DIy = d[Iy]/d[x];
          yplot = plot[x,y];
        DIplot = plot[mids[x],DIy];
        Show[yplot,DIplot];

This user-defined plot function corresponds to the two-argument Matlab function plot(x,y). After completing multiple plots, they can be superimposed by the MathematicaShow function. Except for this difference in multiple plots, Sections 2 through 6 of Sample Calculus should directly transliterate using these definitions. Of course, the Matlab periods are unnecessary since arithmetic operations are automatically listable in Mathematica and function arguments use square brackets.

File sampcalc.nb is a notebook to run the sample calculus functions.