Final review topics
This list is meant to give you an overview of the concepts and techniques that
could be on the ﬁnal (Thursday 5/5 at 9am or (alternative) Saturday 4/30 at
12pm). Questions on the test may combine material from two or more of the
sections listed.
Background
 Basic diﬀerentiation techniques: in particular, the product rule and the
chain rule.
 Basic integration techniques: in particular, integration by parts and inte
gration by substitution.
 Graphing ellipses, circles, hyperbolas and parabolas in simple cases (e.g.
when taking traces of a surface).
Section 13.1
 Distances in two and three dimensions.
 The equation of a sphere, and completing the square to ﬁnd center and
radius.
Section 13.2
 ‘
h
a,b,c
i
’ and ‘
a
~
i
+
b
~
j
+
c
~
k
’ notation for vectors.
 Adding and subtracting vectors, and multiplying a vector by a scalar, and
the geometric interpretation of these operations.
 Basic properties of these operations on vectors (page 810).
 The vector
~
PQ
from a point
P
to a point
Q
.
Section 13.3
 Taking dot products in two and three dimensions, and geometric interpre
tation.
 Using dot products to check for orthogonality.
 The formula relating the dot product of two vectors to the angle between
them.
Section 13.4
 Taking cross products, and geometric interpretation (including the ‘right
handrule’).
 The formula relating the length of the cross product of two vectors to the
angle between them.
1
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View Full Document Relation of the dot product to parallelism.
 The formula for the volume of a parallelepiped in terms of the dot and
cross products.
Section 13.5
 Vector, parametric, and symmetric forms for the equation of a line (in
cluding the ‘direction vector’).
 Finding whether two lines are parallel, skew, or intersect in a unique point
(and ﬁnding the point if it exists).
 The relationship of a normal vector to a plane with the scalar equation of
a plane, and the geometric interpretation of the normal vector.
 Using geometric information about points on a plane, and lines in or par
allel to a plane to ﬁnd its scalar equation.
 Finding the angle between two planes.
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 Spring '08
 ALDROUBI
 Derivative, Polar coordinate system, geometric interpretation

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