MIDTERM 2: Wednesday,
February 17. Important note:
In comparison with Midterm 1, this exam contains topics that are new to
most of you. For this reason the exam will appear more challenging than Midterm
1. Please work hard to prepare yourself well. Topics to be tested on Midterm
2 are listed below. The emphasis will be given on applications such as computing
mass given density, computing work, etc. That is, you will be expected to
interpret the reality using the right kind of integral. Also, you will be
expected to apply the background material that already appeared on Midterm
1, that is, the relevant integration techniques. As in Midterm 1, all integrals
that will appear on Midterm 2 will have sufficiently simple solutions.
Added on Feb 14 at 8:35pm: The format of Midterm 2 will be
the same as that of Midterm 1: There will be four problems, each worth 10
points.
Section 15.1: Vector fields: graphing vector
fields, computing flow lines, computing gradients and potential functions.
Section 15.2: Line integrals with respect
to the arc length (Type I line integrals) and their applications: computing
mass, center of mass, etc. Line integrals for computing work (Type II
line integrals) and line integrals with respect to coordinates. Applications
in computing work.
Section 15.3: Fundamental theorem on line
integrals -- evaluating line integrals for conservative vector fields. Line
integrals along a closed piecewise smooth curve.
Section 15.4: Green's theorem and one
of its applications: Evaluating line integrals using Green's theorem.
PRACTICE PROBLEMS: The following selection picks
one problem from each type you should be able to solve.
Exercises for Section 15.1 (p. 1119): 19, 33, 41
Exercises for Section 15.2 (p. 1134): 3, 9, 18, 23, 27, 34, 35, 51
Exercises for Section 15.3 (p. 1145): 9, 15, 17, 21, 23, 27
Exercises for Section 15.4. (p. 1156): 5, 7, 9, 15