Topics list for final exam-Below I have
listed the main topics from each chapter the final exam covers. Following each is a list of problems dealing
with that topic from the practice problems and practice exams. Some problems are listed in more than one
topic. My notation is: S07 and F06 for
the Spring 07 and Fall 06 exams, PP1, PP2, or PP3 for the practice problems
which are divided into 3 sets. For the
midterm 1 and 2 material, you can find additional problems in the practice
exams and review material posted on the course-wide website for those
exams. For any topic, you can also find
many problems in the book that are related.
If you want some suggestions for problems, email me anytime.
Midterm 1 and 2 Material
Chapter 12-Vectors
and the Geometry of Space
- using
dot product, cross product, geometric reasoning: S07#1a, F06#1a, PP2#7,
PP3#1
- equations
of lines and planes: S07#1a, F06#1a, PP2#7, PP3#1a
Chapter 13-Vector
Functions
- position,
velocity, speed, and acceleration: PP2#6
- tangent
vectors to space curves: PP1#5b
- arc
length (note connection between arc length and line integral with respect
to arc length):
Chapter 14-Partial
derivatives
- tangent
planes and normal lines: S07#1b, F06#1b, PP1#5a, PP2#4
- chain
rule:
- linear
approximations:
- directional
derivatives: PP1#5b, PP2#1
- finding
and classifying critical points (see below):
- Lagrange
multipliers (see below):
- absolute
max and min over a region (often uses both critical points and Lagrange
multipliers): S07#2, F06#2, PP1#6, PP2#5, PP3#2
New Material
Chapter 15-Multiple
integrals
- double
integrals over general regions: PP1#1, PP3#2
- reversing
order of integration: PP1#1
- double
integrals with polar coordinates (note: you often have to recognize that
polar coordinates is the best option): S07#4, F06#3, F06#4, PP1#3, PP3#5
- finding
the volume of a solid: S07#4 , F06#4
Chapter 16-Vector
calculus
- line
integrals with respect to x, y, and z: S07#6, F06#6
- line
integrals with respect to arc length
- line
integrals of vector fields: PP1#2, PP2#2a, PP3#6
- checking
if a vector field is conservative: S07#5, F06#5, PP2#3a
- finding
potential functions: S07#5, F06#5, PP1#4a, PP2#3a, PP3#4a
- using
potential functions to evaluate a line integral: PP1#4b, PP2#3b, PP3#4b
- using
Green’s Theorem to evaluate a line integral over a closed curve: S07#7,
F06#7, PP2#2b, PP3#5