Date Assigned: Monday, April 19, 1999

Date to turn in: Thursday, April 22, 1999

Section 13.7 - 1, 5, 7, 11, 13, 15, 19
 

Read section 13.9 and write a 100 word summary of it.

General Goals for the class:

Note that we are skipping section 13.8 of the text.  It is on partial differential equations.  I think this topic is better covered in a later course.  The material is the analog of the section on differential equations covered earlier.  If you are interested in this section, read it over and look over the problems.  I will be happy to answer questions at the end of class.

Section 13.7 - This section discuses the second derivatives of function of two variables.   We know from previous work that there is only one second derivative of a function of one variable.  It represents the rate of change of the first derivative and one thing it show is the concavity of the graph of the function.  In the case of functions of two variables, there are 4 second order partial derivatives.  There are two mixed partial derivatives, the one where you take the partial with respect to x first then take the partial with respect to y second and one one where take the partials in the opposite order.  Under normal circumstances they are equal.  This section goes into what these second partials might represent and why we might believe that they are equal.