CC
Index
absolute value 31
domain of a function 19
addition function 76
domain of an equation 51
addition of
dot product 82
complex numbers 352
double angle formula 268
Thistext
text
will
beginwith
witha aabrief
briefreview
reviewofof
ofsome
someprecalculus
precalculusmaterial
materialthat
that
addition
of
vectors
74
This
text
will
begin
with
brief
review
some
precalculus
material
that
This
will
begin
you
areassumed
assumed
tobebe
becomfortable
comfortablewith:
with:
quadratic
polynomials,exponenexponenangle
196
ellipse
204polynomials,
you
are
assumed
comfortable
with:
quadratic
polynomials,
exponenyou
are
toto
quadratic
tials,
and
logarithms,
as268
fewexamples.
examples.empty
We’llthen
thensee
seea aabrief
briefintroduction
introduction
angle
sum
formulas asas
set
15
tials,
and
logarithms,
few
examples.
We’ll
then
see
brief
introduction
tials,
and
logarithms,
a aafew
We’ll
toarccosine
linearalgebra
algebra
inthe
theplane.
plane.This
Thisisisisthe
thestudy
studyofof
ofvectors
vectors
inthe
the
plane,ofof
ofthe
the
301inin
equation
of
a circle
187
linear
algebra
the
plane.
This
the
study
vectors
the
plane,
the
toto
linear
inin
plane,
algebra
relating
tovectors,
vectors,and
andofof
ofmatrices,
matrices,
which
themost
mostimportant
important
arcsine
298 toto
equation
ofare
aare
hyperbola
209, 210
algebra
relating
vectors,
and
matrices,
which
are
the
most
important
algebra
relating
which
the
functions
thatare
areused
usedtoto
torelate
relatevectors
vectorstoequation
toeach
eachother.
other.
arctangent
303
of an ellipse 206
functions
that
are
used
relate
vectors
to
each
other.
functions
that
equations equivalent by:
Cartesian coordinates 243
addition 56
coefficient of
invertible function 61
a polynomial 113
multiplication 58
cofunction identity 276
even function 232
column vector 73
complex numbers 349
function 19
composition 28
function in two variables 112
conic 154
cosecant 274
283
sq sq
€ctoCSgraph transformations
€ctoCS
cosine 223
cotangent
274
horizontal
line
testsoso
39
Linearalgebra
algebra
isnot
notthe
theprimary
primaryinterest
interest
ofthis
thiscourse,
course,
sowe’ll
we’llkeep
keepour
our
Linear
algebra
not
the
primary
interest
this
course,
we’ll
keep
our
Linear
isis
ofof
cubic formula
389but
treatment
ofitititbrief,
brief,
butitititwill
willbebe
beimportant
importantfor
forusus
ustoto
tobebe
becomfortable
comfortablewith
with
treatment
brief,
but
will
important
for
comfortable
with
treatment
ofof
identity
228
somebasic
basiclinear
linearalgebra
algebrainin
inorder
ordertoto
tobetter
better
studythe
the
topicsthat
thatthis
thiscourse
course
some
basic
linear
algebra
order
better
study
the
topics
that
this
course
some
study
topics
degenerate
conic
333
identity
function
20
isdevoted
devotedto,
to,namely,
namely,trigonometry,
trigonometry,conics,
conics,and
andthe
thecomplex
complexnumbers.
numbers.
devoted
to,
namely,
trigonometry,
conics,
and
the
complex
numbers.
isis
De Moivre’s Formula 369
identity matrix 89
Trigonometryisis
is the
thestudy
studyofof
oftriangles.
triangles.More
Moreprecisely,
precisely,itititisisisthe
the study
studyofof
of
Trigonometry
study
triangles.
More
precisely,
Trigonometry
determinant
96 the
imaginary
axis 351 thestudy
therelationship
relationshipbetween
betweenthe
the lengths
lengthsofof
ofthe
thesides
sidesofof
ofa aatriangle
triangleand
andthe
the interior
interior
the
relationship
the
sides
triangle
and
the
diagonal
matrixbetween
91 thelengths
imaginary
number
351 theinterior
anglesofof
ofa aatriangle.
triangle.
angles
triangle.
angles
discriminant
6
imaginary part of a
Introduction
Introduction
/
/
distance between points
in the plane 182
division of complex numbers:
Cartesian coordinates
356
bb
polar coordinates 378
complex number 350
implied domain:
of a function 25
of an equation 51
inner product 82
5
CC
CC
integers 12
interval 14
inverse function 43
inverse matrix 94
plane 72
point 72
point-slope form 144
polynomial 20
polynomial equation
law of cosines 252
in two variables 119
law of sines 248
polynomial in two variables 113
linear equation in
POTS 125
Thistext
textwill
willbegin
beginwith
witha aabrief
briefreview
reviewofof
ofsome
someprecalculus
precalculusmaterial
materialthat
that
This
text
will
begin
with
brief
review
some
precalculus
material
that
This
two variables 140
projection
80
youare
areassumed
assumedtoto
tobebe
becomfortable
comfortablewith:
with:quadratic
quadraticpolynomials,
polynomials,exponenexponenyou
are
assumed
comfortable
with:
quadratic
polynomials,
you
logarithm
10
Pythagorean
identity
228exponentials,and
andlogarithms,
logarithms,asas
asa aafew
fewexamples.
examples.We’ll
We’llthen
thensee
seea aabrief
briefintroduction
introduction
tials,
and
logarithms,
few
examples.
We’ll
then
see
brief
introduction
tials,
Pythagorean
Theorem
180
tolinear
linearalgebra
algebrainin
inthe
theplane.
plane.This
Thisisisisthe
thestudy
studyofof
ofvectors
vectorsinin
inthe
theplane,
plane,ofof
ofthe
the
linear
algebra
the
plane.
This
the
study
vectors
the
plane,
the
toto
matrix 87
algebrarelating
relatingtoto
tovectors,
vectors,and
and of matrices,
matrices,which
whichare
arethe
themost
mostimportant
important
algebra
relating
vectors,
which
are
the
most
important
algebra
matrix multiplication
93 andofofmatrices,
quadratic
equation
in
functionsthat
thatare
are used
usedtoto
torelate
relatevectors
vectorstoto
toeach
eachother.
other.
functions
that
are
relate
vectors
each
other.
functions
multiplication
of used
complex
numbers:
two variables
154
Cartesian coordinates 355
quadratic formula 6
polar coordinates 377
multiplicative inverse of a
range 40
complex number in
rational function 26
Cartesian coordinates 356
rational numbers 12
multiplying a row vector and
real axis 351
a column vector 74
real numbers 12
real part of
natural logarithm 129
complex number 350
sq sq
€
ctoCS
€
ctoCS
natural number 12
restricted domain:
nondegenerate conic 333
of a function 22
Linear
algebra
is
not
the
primary
interest
ofthis
this
course,soso
sowe’ll
we’llkeep
keepour
our
Linear
algebra
is
not
the
primary
interest
of
this
course,
we’ll
keep
our
Linearofalgebra
is not
the primary
course,
norm
a complex
number
354 interest ofof
an
equation
52
treatment
ofitititbrief,
brief,
butitititwill
willbebe
beimportant
important
forusus
ustoto
to
becomfortable
comfortablewith
with
treatment
brief,
but
will
important
for
comfortable
with
treatment
but
bebe
norm of aofof
vector
183
right for
angle
197
somebasic
basiclinear
linearalgebra
algebrainin
inorder
ordertoto
tobetter
better
study
thetopics
topics
thatthis
thiscourse
course
some
basic
linear
algebra
order
better
study
the
topics
that
this
course
some
study
the
right
triangle
179that
is
devoted
to,namely,
namely,
trigonometry,conics,
conics,
and
thecomplex
complexnumbers.
numbers.
devoted
to,
namely,
trigonometry,
conics,
and
the
complex
numbers.
isis
devoted
to,
and
odd
function
232 trigonometry,
root
6the
one-to-one
38 isis
roots
of precisely,
unity
373
Trigonometry
isthe
thestudy
studyofof
oftriangles.
triangles.
More
precisely,
thestudy
studyofof
of
Trigonometry
the
study
triangles.
More
precisely,
the
study
Trigonometry
More
itititisisisthe
onto
42
rotation
matrix
266
the
relationship
betweenthe
thelengths
lengthsofof
ofthe
the
sidesofof
of
triangle
andthe
theinterior
interior
the
relationship
between
the
lengths
the
sides
triangle
and
the
interior
the
relationship
between
sides
a aatriangle
and
rotation of the plane 258
anglesofof
ofa aatriangle.
triangle.
angles
triangle.
angles
period 193
row vector 73
⇡ 189
piecewise defined function 29
scalar multiplication 78
planar transformation 98
scalar product 82
Introduction
Introduction
/
/
bb
6
CC
CC
secant 274
set 11
set minus 12
set notation 11
sine 225
slope 141
slope-intercept form 143
solutions
of will
equations
52, aa119
Thistext
text
will
beginwith
with
briefreview
reviewofof
ofsome
someprecalculus
precalculusmaterial
materialthat
that
This
text
begin
with
brief
review
some
precalculus
material
that
This
will
begin
a brief
subset
11
youare
areassumed
assumedtoto
tobebe
becomfortable
comfortablewith:
with:quadratic
quadraticpolynomials,
polynomials,exponenexponenyou
are
assumed
comfortable
with:
quadratic
polynomials,
exponenyou
subtraction
of
tials,and
andlogarithms,
logarithms,asas
asa aafew
fewexamples.
examples.We’ll
We’llthen
thensee
seea aabrief
briefintroduction
introduction
tials,
and
logarithms,
few
examples.
We’ll
then
see
brief
introduction
tials,
complex
numbers
353
tolinear
linearalgebra
algebrainin
inthe
theplane.
plane.This
Thisisisisthe
thestudy
studyofof
ofvectors
vectorsinin
inthe
theplane,
plane,ofof
ofthe
the
linear
algebra
the
plane.
This
the
study
vectors
the
plane,
the
toto
subtraction
of
vectors
76
algebrarelating
relatingtoto
tovectors,
vectors,and
andofof
ofmatrices,
matrices,which
whichare
arethe
themost
mostimportant
important
algebra
relating
vectors,
and
matrices,
which
are
the
most
important
algebra
functionsthat
thatare
areused
usedtoto
torelate
relatevectors
vectorstoto
toeach
eachother.
other.
functions
that
are
used
relate
vectors
each
other.
functions
tangent 236
target 19
term of a polynomial 113
triangle 179
trigonometric identity 308
Introduction
Introduction
/
/
union 149
unit circle:
of complex numbers
of vectors 187
363
sq sq
€ctoCS
€ctoCS
vector 72
Linearalgebra
algebraisis
isnot
notthe
theprimary
primaryinterest
interestofof
ofthis
thiscourse,
course,soso
sowe’ll
we’llkeep
keepour
our
Linear
algebra
not
the
primary
interest
this
course,
we’ll
keep
our
Linear
treatmentofof
ofitititbrief,
brief,but
but itit will
will be
be important
important for
for us
us to
to be
be comfortable
comfortable with
with
treatment
brief,
but
treatment
winding function
191 it will be important for us to be comfortable with
somebasic
basiclinear
linearalgebra
algebrainin
inorder
ordertoto
tobetter
betterstudy
studythe
thetopics
topicsthat
thatthis
thiscourse
course
some
basic
linear
algebra
order
better
study
the
topics
that
this
course
some
isdevoted
devoted to,
to,namely,
namely,trigonometry,
trigonometry,conics,
conics,and
andthe
thecomplex
complexnumbers.
numbers.
devoted
namely,
trigonometry,
conics,
and
the
complex
numbers.
isis
zero of a to,
function
312
Trigonometryisis
isthe
thestudy
studyofof
oftriangles.
triangles.More
Moreprecisely,
precisely,itititisisisthe
thestudy
studyofof
of
Trigonometry
the
study
triangles.
More
precisely,
the
study
Trigonometry
therelationship
relationshipbetween
betweenthe
thelengths
lengthsofof
ofthe
thesides
sidesofof
ofa aatriangle
triangleand
andthe
theinterior
interior
the
relationship
between
the
lengths
the
sides
triangle
and
the
interior
the
anglesofof
ofa aatriangle.
triangle.
angles
triangle.
angles
bb
7
CC