Multivariate Calculus - Bruce E. Shapiro
Multivariate Calculus - Bruce E. Shapiro
Multivariate Calculus - Bruce E. Shapiro
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
viii<br />
CONTENTS<br />
Symbol<br />
Table 1: Symbols Used in this Document<br />
Description<br />
F, G(x, y, ..),. . . Vector function, with or without explicit variables.<br />
f ′ , f ′ (x), df/dx<br />
f : D ↦→ R<br />
f : R n ↦→ R m<br />
lim x→y<br />
u, v, . . . vectors<br />
u · v, p · q,. . .<br />
u × v<br />
P, Q, . . . points<br />
PQ, RS,. . .<br />
−−→<br />
PQ,. . .<br />
the derivative of f with respect to x<br />
the function f has a domain D and a range R<br />
the function f has an n-dimensional domain<br />
and an m-dimensioned range.<br />
the limit as x approaches y<br />
dot product between vectors<br />
cross product between vectors<br />
line segments between points<br />
vector from P to Q<br />
R, R 2 , R 3 real numbers, real line, 3D space<br />
R n<br />
n-space<br />
x, y, z,. . . variables<br />
|x|, |f(x)|,. . .<br />
‖v‖, ‖F(x, y, z)‖,. . .<br />
⎛ ⎞<br />
(x, y), 〈x, y〉, ⎝ x ⎠<br />
y<br />
⎛ ⎞<br />
x<br />
(x, y, z), 〈x, y, z〉, ⎜y⎟<br />
⎝ ⎠<br />
z<br />
⎛ ⎞<br />
a b c ⎛ ⎞<br />
⎜d e f⎟<br />
⎝ ⎠ , ⎝ a b ⎠<br />
c d<br />
g h i<br />
absolute values<br />
vector norms<br />
two-dimensional vector with components x and y<br />
three-dimensional vector with components x, y, z<br />
Matrices<br />
Revised December 6, 2006. Math 250, Fall 2006
Change language