math_for_programmers.pdf

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3D graphics, machine learning,
and simulations with Python
Paul Orland
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Mathematical Notation Reference
3
Mathematical Notation Reference
Notation example
(x,
y)
sin(x)
cos(x)
θ
π
(x,
y, z)
u
·
v
u
×
v
f
(g(x))
f
(x,
y)
versus
f
(x)(y)
au
+
bv
e
1
,
e
2
,
e
3
, . . .
⎛ ⎞
1
⎝
2
⎠
v
=
3
⎛
1 2
⎝
4 5
A
=
7 8
R
n
(f +
g)(x)
or
f
(x) +
g(x)
c
·
f
(x)
span({u,
v, w})
f
(x) =
ax
+
b
f
(x) =
a
0
+
a
1
x
+
· · ·
+
a
n
x
n
⎞
3
6
⎠
9
Name
Coordinate vector in 2D
Trigonometric sine function
Trigonometric cosine function
Greek letter
theta,
commonly representing angle measure
Greek letter
pi,
representing the number 3.14159
. . .
Coordinate vector in 3D
Dot product of two vectors
u
and
v
Cross product of two vectors
u
and
v
Composition of functions
See discussion of
currying.
Linear combination
two vectors
u
and
v
Defined in section
2.1.1
2.3.1
2.3.1
2.3.1
2.3.2
3.1.1
3.3
3.4
4.1.2
4.1.2
4.2.3
4.2.4
5.1.1
Standard basis vectors
Column vector
Matrix
Real coordinate vector space of dimension
n
Adding two functions
Scalar multiplication of a function
The span of a set of vectors
Linear function
Polynomial function
5.1.1
6.2.1
6.2.3
6.2.3
6.3.3
6.3.5
6.3.5
(continues on inside back cover)
Math for Programmers
3D graphics, machine learning and simulations with Python
ii

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