Math 234 — About the Exams

• Final
• Midterms
• Quizzes

The Final

Location

• If Brandon Alberts is your TA then go to room 5106 in the Social Sciences building.
• All other students should go to room 6210 in the Social Sciences building.

Office hours

Topics covered

• Parametric curves: know how to parametrize a straight line, a line segment connecting two points, a circle. Find the unit tangent and normal to given parametrized plane curves.
• Chain rule for $g(t) = f(x(t), y(t))$, or $g(u,v)=f(x(u,v), y(u,v))$; second derivatives too. For practice see the old exams.
• Clairaut’s theorem, and how to find a function $f(x,y)$ if you are given its partial derivatives $f_x(x,y)=P(x,y)$ and $f_y(x,y)=Q(x,y)$. Note the even though there may not be an explicit question of this form on the exam, knowing how to find $f$ can be very useful when doing line integrals.
• Maxima and minima of functions of two or three variables (the theorems: continuous function on a closed and bounded set always has a max and a min; if a max or min is an interior point, then it’s a critical point)
• Second derivative test (say in words why it works? Know how to analyze the second order terms by completing a square)
• Lagrange multipliers (don’t forget the so-called “exceptional case”)
• Double & Triple integrals (finding the integration bounds from a drawing or description of the domain; drawing the domain given the integration bounds; changing the order of integration)
• Know that $\int_\cC1\,ds$ is the length of the curve $\cC$, $\iint_\cR1\,dA$ is the area of the two dimensional region $\cR$, and $\iiint_\cR 1dV$ is the volume of $\cR$ if $\cR$ is a three dimensional region.
• Polar, Cylindrical, and Spherical Coordinates (recognize regions that are “blocks” in either cylindrical or spherical coordinates; understand the drawings that shows $dA=r\, dr\,d\theta$, $dV=r\,dz\,dr\,d\theta$, and $dV = \rho^2\sin\phi\,d\rho\,d\theta\,d\phi$)
• Line integrals (work and flux integrals; differential form version) and Green's theorem: the two forms (“work” and “flux” integrals). The fundamental theorem (about the line integral when the vector field is the gradient of a function.)
  See a short summary of line integrals and the Extra problems about line integrals (with answers)

Old final exams

Midterms

Midterm 3— Monday, November 20

Topics: See the study guide for the list of topics covered on the third midterm.

Midterm 2— Wednesday, October 25

Topics: See the study guide for the list of topics covered on the second midterm.

Midterm 1— Wednesday, September 27

The exam with solutions (pdf).