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\tfd Using Technology \blank
\tfd in\blank
\tfd Teaching Multivariable Calculus\vfill
\tfb David Arnold\vfill
\tfb Humboldt Mathematics Colloquium\blank
\tfb\currentdate[month,year]
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\subject{Matlab}

In order to use Matlab effectively, students must understand that
Matlab's basic data structure is the matrix.

\startitemize

\item Entries in rows are separated by commas.
  \starttyping
  >> u=[1,2,3]
  u =
  1            2            3    
  \stoptyping

\item Rows are terminated by semicolons.
  \starttyping
  >> v=[1;2;3]
  v =
  1      
  2      
  3   
  \stoptyping

\item Row entries can also be separated by spaces.

  \starttyping
  >> A=[1 2;3 4]
A =
      1            2      
      3            4     
  \stoptyping

  \stopitemize


\page
\subject{The Algebra of Vectors}

\startitemize
\item Vectors are added element by element.
  \starttyping
  >> u=[1,2,3]; v=[4,5,6];
>> u+v
ans =
      5            7            9     
  \stoptyping
\item Vectors are subtracted element by element.
  \starttyping
  >> u=[1;2;3]; v=[4;5;6];
>> u-v
ans =
     -3      
     -3      
     -3    
  \stoptyping
\item Scalar multiplication is performed on each element.
  \starttyping
>> u=[7,8,9];
>> 2*u
ans =
     14           16           18    
  \stoptyping
\stopitemize

\page
\subject{Matrices}

\startitemize

\item Matrices of equal size are added (or subtracted) element by element.
  \starttyping
  >> A=[1,2,3;4,5,6]; B=[1,1,1;2,2,2];
>> A+B
ans =
      2            3            4      
      6            7            8  
  \stoptyping

\item Scalar multiplication is performed on each entry.
  \starttyping
>> A=[1,2;3,4;5,6;7,8];
>> 2*A
ans =
      2            4      
      6            8      
     10           12      
     14           16  
\stoptyping

\stopitemize

\page
\subject{Unorthodox}

Subtracting a scalar from a matrix or vector makes no sense
mathematically.
\startformula
\left(\matrix{1 & 2 & 3\cr 4 & 5 & 6}\right)-1
\stopformula
However, this is such a common occurrence, Matlab interprets this to
mean
\startformula
\left(\matrix{1 & 2 & 3\cr 4 & 5 & 6}\right)-1=\left(\matrix{0 & 1 & 2\cr 3 & 4 & 5}\right).
\stopformula
\page
\subject
{Parametric Equations}


\stoptext