I am excited about starting my second tutorial on another
subject. My first one was intended for less knowledgable people
in math. This one is intended for more serious learners in
mathematics. Since there are more people who use math for
applied reasons and because it is easier to learn than pure
mathematics I decided to go with the greater good and type one
closer to applied math. It is assumed that the reader is well-
versed in Multivariable Calculus, has a good understanding of
multiple integration and partial differenciation. This first
lecture will be on Change of Variables. I choose this topic
because it is usually not studied in a standard Calculus
sequence and because I happen to think it is very useful at
times. In single variable calculus if you have the integral of
the form then by defining this integral reduces to , this is the
all popular and useful Substitution Rule. In multivarible
calculus we have a similar situation with changing variables.
However, things get inevitably more complicated beca