Math 251-502 Test 1 Review
General Information. Test 1 will be on Wednesday,
2/20/08. Please bring an 8½×11 bluebook. To get some idea
of what the test will be like, look at
exams I and II on the math department's 251 web page. Be aware
that these cover a somewhat different selection of topics and are
definitely not the same as what your test will
be. There is a
Math 251 help session. The one closest to the test will be this
Sunday (2/17/08), 6-8 pm, in BLOC 164.
Extra office hours. In addition to my usual MWF office hours, I
will have extra office hours on Tuesday (2/19/08), from 10-12.
Material covered.
-
Chapter 11
- Sections 11.1 through 11.3. Be very familiar with notation for
vectors. You should know what the dot and cross product are and what
their geometric significance is. Be able to use them to find
geometric quantities, such as angles between vectors, scalar and
vector projections, areas of triangles, and volumes of
parallelepipeds.
- Section 11.4. Be able to find equations of lines and planes. In
addition, know how to find distances between points and planes,
parallel planes, skew lines. Also, be able to find the angle between
planes.
- Section 11.5. Be able to classify quadric surfaces and to make
rough sketches of them.
-
Chapter 12
- Sections 12.1 and 12.2. Know what the domain and range of a
function are, and know how to find the domain in simple
cases. Concerning limits and continuity, be able to problems similar
to those for homework, for examples given in class, or examples in
the text.
- Sections 12.3 and 12.4. Know the notation for partial
derivatives, how to compute them, and how to find mixed partials
using Clairaut's Theorem. It's a good idea to review the basics of
differentiation you learned in the first two semesters of calculus,
including derivatives of logs, exponetials, trig functions, and so
on. Be able to use partial differentiation to find tangent planes and
differentials. Know how to use differentials to estimate small
changes in a quantity due to small changes in values of variables.
- Section 12.5. Know the chain rule and the Implicit Function
Theorem. Be able to use these to find partial derivatives of
composite functions and implicitly defined functions.
- Section 12.6. Know how to find directional derivatives and
gradients and how to use them to find diections of maximum and
minimum increase for a function at a given point. In addition, be
able to find tangent planes and normal lines for implicitly defined
surfaces.
- Section 12.7. Be able to do max/min problems, including word
problems, and to use the second derivative test to check whether a
critical point is a maximum, minimum, or a saddle point.
Calculators. You may use calculators that do scientific
calculations -- sines, cosines, logs, arithemtic, etc. --, although
you will not need them. You may not use any calculator that
has the capability of doing algebra, calculus, graphing, or of storing
material.
Other devices. You may not use cell phones, computers,
or any other device capable of storing, sending, or recieving
information.
Structure. There will be 6 to 8 questions, some of which will
be fill-in-the-blank questions. The problems will be similar to ones
done for homework, or done as examples in class or in the text.
Updated 2/15/08 (fjn)