First Midterm: during class on Wednesday, October 2, 2013
The midterm covers Chapter 1, 2, and 4 of the text.Doing all of the homework problems prior to the exam is a very good idea. Doing additional problems from the text can be helpful. Here is a list of topics you should know.
If you wish to use a calculator on the exam you may, although it is by no means necessary and unlikely to be of any help: all problems may be readily done without one.
Sample exams Here are two exams given in MAT307 over the past couple of years. Solutions will arrive later, to help encourage you to do the problems on your own.

Fall 2010 [last time I taught this course]; here are the solutions
On this test, the mean was 53 out of 74(a B); the A,A grades were 65 and up. Students needed at least 40 for a C. 
Fall 2011 [given by Prof. Anderson]; here are the solutions.
I don't know what the grade distribution was like, but this seems to be about of comparable difficulty to the other test. I would guess the mean was about 65 (out of 90) and the pass line around 45 or 50.
Below is a graph of the grade distribution on the exam.


You can check your grade here.
Here is a copy of the exam so you can relive the magic. Also, here are the solutions to the exam.
Second Midterm: in class on in mid November (probably)
The second midterm will cover the material we have covered since the first
exam: chapters 5 and 6, and the beginning of chapter 7.
Maybe this exam will be a bit more challenging than the first exam.
As on the first midterm, a calculator is allowed but almost certainly of
little use.
Sample exams
Here are two exams given in MAT307 over the past couple of years. Solutions
will arrive later, to help encourage you to do the problems on your own.
Results:
Some people did well on the exam, but many did much less well.
Three people had no points taken off.
Below is a graph of the score distribution on the exam.


You can check your grade here. If you got a C or lower on the exam, you will need to make some significant changes if you expect to pass the course, even if you are getting an A on homework (a lot of people are).
Here is a copy of the midterm.
Final Exam: 8:30pm on Tuesday, December 10, 2013
The final will be cumulative, covering everything that we have done in the
class. However, extra emphasis will be on material since the second
midterm (material in chapters 7, 8, and 9).
As on the midterms, you can use a calculator if you want, but I really don't
see the point.
Sample exams Here are two final exams given in MAT307 in the past two years, both by Prof. Anderson. There is some overlap in the problems, and both have Stokes theorem questions; we won't have Stokes theorem, but expect at least one Green's theorem question.
Aurélien will hold a review session Monday, Dec 9 from 56:30pm in Physics P113. I will have office hours on Tuesday, Dec 10 from 9:3012:30 and 2:303:30 for lastminute questions.
List of topics for final.
The final will cover everything we have done in the class, with an emphasis
on the material since the second midterm (that is, integration, vector
fields, etc.).
Make sure that you know:
 stuff about vectors (dot and cross products,vector valued functions, vector fields) and matrices; how to calculate with them, including products, inverses, etc.
 equations of lines and planes in several variables.
 curves in the plane and space; derivatives an tangent vectors, arc length, curvature.
 functions of several variables, both graphs of functions of several variables and parametric surfaces.
 partial derivatives, tangent planes, the derivative matrix, implicit differentiation.
 max/min of functions of several variables (including Lagrange multipliers), locating and classifying critical points.
 multiple integrals; calculating volumes. Polar, spherical, cylindrical coordinates, as well as general change of variables (ie, Jacobi's theorem). Imporper integrals.
 Vector fields: line integrals, divergence, curl, Green's theorem, potential functions, conservative vector fields and independence of path.
 While you won't be asked to use Stokes' theorem or Gauss' theorem, you should know what the divergence and the curl of a vector field in the plane and in space is.